Sourdough starter confusion

First,  you are in a great place with Hamelman, I think that is the best book to work from.  OTOH,  he does not spend many pages on sourdough. Also, if you ask a question about sourdough to a 100 bakers, you will likely get several hundred different answers.  Here are mine.

Many people use the same words to mean different things, and others use different words to describe the same thing, which can add to confusion.

From your description, it appears the phrase levain is the stuff that will be added to the dough to make it rise in the place of commercial yeast,  and the starter is what is fed from time to time, and a part of which will come out and be used to make the levian.

Using those terms, you can make a very small starter ( I normally keep 15 grams on hand,  though others keep more)  One way to think about it is that every feeding cycle, you will take the existing starter, throw out all but 10 grams, then add water and flour to that 10 grams of existing starter.  When the starter has consumed that food, you feed it again. Right before each feeding, the jar has a ton of yeast ready to develop, but no food.  The instant you refresh it,  it has a much lower percentage of yeast, but a lot of food that the yeast can thrive on.   This  process of feeding repeats indefinitely - the time in between feeding depends on a number of factors, including the temperature.

Once you feed it, also called a refresh, it goes through a process where the existing starter starts to consume the added water and flour, and it will increase in volume until eventually it will stop rising, and then start to fall.  When it is used to make bread at that stage of development ,  it is called mature.  Some use it earlier than peak -others use it well after it peaks-  and that will impact the taste as well as how the dough rises.   If you used all the starter to make a loaf of bread, you would have a nice loaf of bread, but then you would have no starter left to bake again. 

To avoid this problem, during a refresh, we retain more starter, and add more flour and water -  we could just keep it together, but often, we split the refreshed starter into 2 jars -  which are two separate branches of that tree .  They are identical in every way,  except that the jar that you called the levian , once it has matured, will all go into the dough to make bread, and that branch will die out.  The other jar, I am calling it a starter, will be refreshed after it matured.

So to answer your questions

1 -  You can keep a much smaller amount of starter than many books recommend.  Some retain a larger amount because they need more.  For me, it is so easy to develop a large amount in a few cycles of feeding  ( by not throwing out the mature starter ) and I bake only once a week, it does not make sense to keep a lot.

2. what should i do with my 280 g of mature starter? You can't use the discarded mature starter in place of flour in a recipe.  Immediately before you refresh a starter, you normally take out a part of the mature starter, to avoid having tons of starter lying around.  The part you take out is sometimes called spent starter, and there are some uses for it.  In general it would not be good for bread - since it is spent, the yeast cells have consumed all the available food in the mature starter, so you would not get much lift.  Some use it for pancakes.  I avoid having lots of spent starter by keeping the grams very low. 

3 why should I use a little amount of starter and feed it with flour before baking instead of using mature starter for baking, and use leftover to cultivate into new starter for next week.  I am not sure I understand this question,  but if you are asking if you could take the levian branch and keep that on hand ,  and refresh it at next feeding, and instead use the spent starter instead of the levian to bake a loaf, yes you can.  Think of it this way,  the loaf is just a refreshment of the starter on a larger scale -  you are adding flour and water, and feeding it, and then baking it.

4.. what is the difference between using mature starter, and preparing levain day before baking with little amount of starter  I don't think there is any difference.  Note that many store their starter in the refrigerator between bakes, to reduce in feeding cycles.  While you could take the mature starter out of the fridge and use it to make bread, many believe that if you give it a refresh  ( adding flour and water and letting it come to a peak ) it will perform better.

4. What impact on finished product rye flour in levaining agent would have?  Some say you should keep separate starters for different percentages of flour - so a separate rye starter and a separate AP starter, etc. Adding different flours to the starter will change its flavor profile slightly, and its leavening properties.  You will have to play with it to see what you like. 

Barry

there is a ridiculous amount of waste suggested in many of the bread cookbooks. The recipes are excellent, but I believe the authors’ commercial bread baking background influence the large volume. For home baked bread, starters need to be scaled down exponentially.

I posted a link to zero waste sourdough. It is excellent, and you can use that for any sourdough recipe.

I maintain a Very small amount of sourdough starter in a very small bowl. The night before I’m going to make SD bread, I take the starter out of The refrigerator, scoop it into a larger bowl, add and mix enough flour and warm water to get the amount I will need for my recipe. cover bowl with a plate

in the morning, I make sure to scoop out a big tablespoon and put it in the cleaned small bowl. cover.

and the cycle continues.