So 1/2 only work if it's within the round.
1: Every time the fighting starts any item actions done in the previous round are locked.
A simple Undo item placement button would work fine. This wont take away from the risk of carry builds as zPity mentioned and it could allow for people to remove items from carousel champions and not just search for an item and feel bad about getting a champion you don't want to put an item on.
2: An undo sale would be nice for those mis-clicks, these could just be active until the shop resets automatically. Would be extremely nice as I have made this mistake a lot and it just feels bad to miss out on something exclusively due to being over the wrong champion. (or selling your 3 star Lissandra because she is freakishly tall in this mode...)
3: Yes plz, I would like it so show champions taken/remaining, but I don't know if people care about the keeping them secret for some reason.
4: Unfortunately, this would be hyper busted. At first I thought you just mean organizing cards by value. Like instead of 13152 it's 11235, but a feature that allows you to just rush level 4/5 units lock them in and win is not even remotely close to fair.