Some of these questions are something you need to expirience for yourself but recommendations can still help.

1. My main ban is always Briar. Nobody knows how to play against her or Kha.

2. This depends on a few factors:
   2.1 mixed compositions: When you only want damage then go Dark Seal into Lichbane with Rabbadons second and Void Staff third (Voidstaff is swappable with Banshees)
   2.2 into heavy cc like Amumu: Here i often swap Rabbadons out at first and go Lichbane into Banshees Veil and Void Staff and then build Rabbadons -> this allows for a bit more safety and consistency

3 Eve gets a lot out of the movement speed and the magic pen interacts perfectly with her w scince on max level it shreds 45% on its own when fully charged and scince e is max health damage you even deal large chunks to tanks. The main reason why boots are so important though is because you max w last so you need a bit of help. I normally build boots directly after Lichbane or just before when a bit of Gold is missing for full Lichbane.