gift for niece

A grain mill is a great tool, and there are many here that would love such a gift,  since the flour tastes better than store bought.  However, it is not really possible to make all purpose flour with a home mill, you need specialized equipment to do that.   The normal trajectory is for someone to start baking bread using store bought flour, and sometimes a bread machine or a no knead loaf, then over time, starting to switch from bread baked in pans ,  to free form  loaves,  then switching from commercial yeast to sourdough starter AKA wild yeast,  then switching to home milled flours, typically white or red whole wheat.   So if she is not into baking bread at all,  you may be throwing her into the deep end, and it may sit unused.     A friend turned me on to home milling many years ago, and I am a zealot about milling, I almost never buy flour at a store,  and never buy bread,  since home milled tastes so much better to me.   OTOH,  your goals for her may be a little too high since home milled wheat is a bit tougher to learn how to bake with.     

In an _introductory_  bread-making class, I believe they will not be covering how to mill flour at home, nor how to bake with home-milled flour (it's different), nor how to choose what wheat to buy, and how to store it. Those would be considered advanced topics.

Q#2: Baskets/bannetons are still needed when you have a proofer.

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I still think you are "putting the cart before the horse".   If you respect your niece, please let her choose the equipment before you buy things.  She may have other priorities.  

Question #1. What are your thoughts on which mill to get from the above three mills?

I think she would do fine with any of the 3. I have a Komo, and it works fine, had a Nutrimill Harvest, which is very similar to the Komo and the Mockmill.  All 3 work the same way,  cleaning is not required all that regularly, and the power is not that big a deal in that at worst, it will take a little longer to mill.  I would save your money and buy the Mockmill 200 if that is much cheaper than the others. Spend some of the savings on the Fourneau or Challenger listed below.

Regarding the Brod & Taylor folding proofer, I found a link to a list of essential baking tools:

https://modernistcuisine.com/tag/baking-tools/

Question #2. Is the folder proofer recommendation supposed to replace the number 2 item on the list in the link above, Baskets?

I am not a big fan of that list, but the proofer does not replace number 2 baskets.   A proofer is used to keep a constant temperature ( warmer than room temperature ) usually while the dough is in bulk fermentation, which is typically done in a plastic or glass container.  Once bulk fermentation is over, dough is divided ( if BF included enough dough for more than one loaf), then shaped, then put in a separate container for final proof.  A basket or couche in often used for final proof.  While it is common to use a retarder for final proof  ( a wine cooler works great for this ) I don't know many who final proof in a proofer. Many people bake lots of loaves and never use a proofer. To me, a proofer would be a luxury, though there may be some who disagree.

Instead, I think you would do well to get her some berries to start grinding -  25 lbs of Hard White and 25 pounds of Hard Red would be a good start, though you might want to add some others like Kamut.

She may also benefit from sourdough -   https://sourdo.com/cultures/    I like the Original San Francisco, but she may like the France culture as well, 

Spend some of the proofer money towards the Fourneau or Challenger. 

Question #3. Would you say this list is complete regarding the extras that I need to ensure my niece has?

If she is making free form loaves, like a batard or baguettes ,  she would appreciate a couche,  https://www.sfbi.com/baking-supplies/linen-canvas-couche  a peel  https://smile.amazon.com/EXO-Non-Stick-Super-Peel-Composite/dp/B00CLS8LLE/ref=sr_1_1?dchild=1&keywords=super+peel&qid=1597190619&s=home-garden&sr=1-1, a pizza stone or steel, a scraper, a mixer, and a digital scale  https://www.amazon.com/My-Weigh-KD-7000-Kitchen-Digital/dp/B01G4EI5DE/ref=asc_df_B01G4EI5DE/?tag=hyprod-20&linkCode=df0&hvadid=225339663785&hvpos=&hvnetw=g&hvrand=8152129876346014427&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9008533&hvtargid=pla-368600719899&psc=1

If she wanted to make boules, she would not need the couche or stone, but would want baskets and a combo cooker and a set of oven safe gloves.   

She would not need the baking pan unless she wanted to make quick breads, like banana bread. While a few suggest a thermometer is handy, many others suggest that temperature does not tell you that bread it done, so that is definitely not necessary.  A timer and a lame are both helpful and pretty inexpensive.   A serrated knife for cutting bread is very helpful  - this one is pretty popular. https://smile.amazon.com/gp/product/B000PS1HS6/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

 I don't anyone that has a bench brush, while modernist bread is probably a fine book, extremely few bakers have it. 

If she is making boules in the combo cooker, she likely will not need a source of steam, since the combo cooker traps in the steam.  If you expect her to bake baguettes or batards, a closed container that traps moisture would be helpful .  One option is the fourneau  https://www.fourneauoven.com/  ,  or the Challenger Bread Pan  https://challengerbreadware.com/product/challenger-bread-pan/     both are quite expensive, and she would only need one,  but she would use it with nearly every bake,  in contrast, she may use the proofer for only a few types of bread. 

Hope she appreciates your gifts,  what ever you get her, and you can always buy some now, and once she has spent some time baking, she may tell you that there are some things she needs  ( like a retarder, or a proofer ) rather than buying things she may never need.  It is like buying her a car - if she wants it to transport one or two people, a sports car might work, if she is regularly transporting 4, a sedan, if she needs to move lots of kids and their things, a minivan, if she wants to go off road, a 4 wheel drive may make sense.  There are many different paths in baking, it is hard to predict which one she will pursue, so don't try to outfit everything.  Many start with a bread machine, a set of measuring cups, and store bought flour and yeast and are quite happy with the results.  

"The flour the Royal Lee produces is supposedly the same as (or nearly the same as) store bought flour."

That's just marketing BS. It is not true in any practical sense.  Fresh-milled is much better, and needs to be handled differently.

It may be able to replicate a fine grind (particle size) of commercial whole grain flour, but it is the _freshness_ of home-milled flour that makes the big difference.  And it is more than just about taste.

Store-bought whole grain flour has sat around warehouses and grocery store shelves for months, and volatile parts of the natural oil in the bran and germ evaporate, and the flour otherwise ages, and the enzymes usually degrade too. This alone dictates different handling.  Recipes/methods must be modified. 

The challenges of switching from store-bought whole grain flour to fresh-milled whole grain flour, are common questions on this web site.

It is also possible/likely that an introductory bread class won't even delve into whole grain flour. 

I admire your desire to be generous to your niece.  But, please let her take small steps first. Hold back on the grain mill until she gets her feet wet.

Barry also has good advice. Let her determine which styles or methods of bread making to pursue, and then help her after she decides what she wants.

If by "studio" you meant "studio apartment" she will be short on space for all the equipment you want to shower her with.

She is blessed to have such a generous benefactor!

I have the earlier version of the Lee, and while it does make a very fine flour, as Dave says, that flour is not the same as store bought flour.  While the taste is far superior, IMO,  Dave is correct that baking with 100% home milled flour is quite challenging.  If you do go with a mill as a gift, your niece may be better off starting with a mix of 25% or slightly more home milled, and the rest AP or Bread Flour.  

Okay,  lots of great questions,  I will take a stab

Mill -  yes plastic Mockmill.  The nicer looking mills are supposed to be kept on the counter.  I mill more than most here  ( I only use 100% home milled for bread, quick breads, pizza, and pasta ) and even I can't justify keeping it on the counter ) So get plastic, it will be lighter, and she definitely won't be using it it every day.

Couche -  can be used for one or multiple batard or baquettes, it will take up less space than a basket - banneton.  Not ideal for boule -  round shaped loaf, but could work to line a collander to final proof for a boule.

Peel -  helpful for batards or baquettes, to take it from the couche and deliver it to the pizza stone.  No absolutely needed -  a pizza peel is actually not ideal,  instead a transfer board would be helpful https://www.amazon.com/Baguette-Transfer-Flipping-Industrial-professional/dp/B07HNL7M5X/ref=sr_1_1_sspa?dchild=1&keywords=baguette+board&qid=1597451199&s=home-garden&sr=1-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExNDhCRFFQSVBOVVVOJmVuY3J5cHRlZElkPUEwNjI0NTEyMVZTNEVKVUNNQTRWUiZlbmNyeXB0ZWRBZElkPUExMDIxMzEyMVA4Mjg1SkZRVk8zUiZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=  again, it depends on what shapes she would like to make.

Pizza Stone -  not needed if she is going to use the Challenger, or combo cooker.  Can be helpful if she is cooking in her Breville Air oven - though frankly, that may be a big challenge -  if the upper element comes on, that will make it difficult to avoid burning the top of the loaf.  Does she have a regular oven as well as the countertop one?   The biggest impact on her loaves will come not from the tools used to mix or proof the dough, but the cooking environment.  An enclosed cooking vessel - Challenger, Dutch Oven, etc, will have a much greater impact than the other things on the list.

Casserole dIsh -  when we talk about bread, we normally refer to breads either baked free form - baguettes,  batards, boules, or sometimes in pans - like sandwich loafs. In general, glass is not a great medium.  The Dutch Oven ( DO ) would be fine, except that the primary reason we use a DO  ( like the combo cooker ) is to keep the lid on for the first part of baking to keep the loaf moist and allow it to expand - called oven spring.  Part way through we take off the lid and let the crust form and brown. So the DO will not be of much help with the top off. Likewise, the casserole would be fine for a boule - though you would need a tight sealing top to keep in the moisture - which is why we like the cast iron DO or combo cooker. 

Timer -  agreed she can use her phone - it just helps to have an alarm to remind her to check the oven to see if the bread is done.

Lame - again not necessary -  some just use a sharp knife -  this is a very nice lame as well https://smile.amazon.com/gp/product/B079G7WC79/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

Bread Knife -  I am not familiar with the one you posted, though I would like at least a 10 inch knife.

Challenger -  she will definitely want an enclosed cooking chamber -  note that ideally it fits with room around it,  since part way through cooking she will need to open the oven door and take off the lid.

Berries, while you addressed it to Ciabatta,  I don't think there would be an objection to me responding.  If they are stored in an airtight container away from light, they can last years.  If she decides she likes to use home milled grain,  plastic food storage containers ( 5 gallons is a popular size ) and gamma lids https://smile.amazon.com/Gamma-Vittles-Stackable-Airtight-Container/dp/B007KAY4S2/ref=sr_1_2?_encoding=UTF8&ascsubtag=1ba00-01000-a0047-win10-other-smile-us000-gatwy-feature-SEARC&dchild=1&keywords=gamma+lid&qid=1597452537&sr=8-2&tag=amz-mkt-chr-us-20 are a good choice for storage.  

If she has not attending the baking class yet,  an online class may be a good way to get her started so that she gets the most from the class.   I found this pretty  helpful  https://shop.mybluprint.com/baking/classes/artisan-bread-making/35515  While some think this book is a little to professional oriented, many of us consider it to be the bible  https://smile.amazon.com/Bread-Bakers-Book-Techniques-Recipes/dp/1118132718/ref=sr_1_1?_encoding=UTF8&ascsubtag=1ba00-01000-a0047-win10-other-smile-us000-gatwy-feature-SEARC&dchild=1&keywords=bread+jeffrey&qid=1597452692&sr=8-1&tag=amz-mkt-chr-us-20

I think I hit each of the issues -  you also mentioned pizza oven, though I did not suggest that.  The Ooni is good for pizza, though not helpful for bread.   And don't forget oven safe gloves -  These are the ones I have https://smile.amazon.com/Grill-Armor-Resistant-Waterproof-Gloves/dp/B078WDR6DR/ref=sr_1_3_sspa?dchild=1&keywords=oven+safe+gloves&qid=1597452926&sr=8-3-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExWFRDUlQwUFRTUVNRJmVuY3J5cHRlZElkPUExMDQ4MDg4MkFWQjEwWDBGVjA2SyZlbmNyeXB0ZWRBZElkPUEwMzY1MDA0MzRTNVo4VUFaUlVRUSZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=  there are some downsides to them, but they are the most heat resistant I can find,  you can pick up a 500 degree cast iron skillet and your hands will not feel like it is even hot.  

Any more questions,  fire away.