Why not ? Infact it is already happening before . one example is on our country most banks here were already partnered with bitcoin and for sure that is also happening on other countries as long as the country is not restricting or banning the use of cryptos .
I don't think so about this. Any transaction that you're going to undergo with BANKS has HIGH transaction fees.
That depend on every bank . some bank only charge a cheap fee for every transaction while some will depend on the amount that you transact but i dont know in the future , maybe banks will be basing their fees thru the recomended fees for bitcoin transactions .