Generally speaking, heights constraints are rare in real life. I would rather keep my beam as a deeper singly reinforced beam rather than a short doubly reinforced beam. Per theory, you can use doubly reinforced beams where there is height restriction.
Read ACI Chapter on development lengths.
Keeping same diameter bar is preferred as it is less work for construction and makes things simple. You are correct in pointing out that books don't show a practical approach towards design when mixing different bar sizes.
Depends what you choose.
Look up a text book. Macgregor has some examples.
We don't.
It can't be. There might be some application under Strut and Tie Model but not in general.
I would just like to add that please don't group your questions in one thread. I have answered your questions but generally I have seen such threads go unnoticed as there are too many offshoots to answer and its hard to tag a thread with a specific category if it has many questions.