Hello,
Is this inspired by brothers??? Anyways, down to the nitty gritty.
1. You can set up a bool system for the player being over it, so basically what you have to do is set both players to have the same tag, then have the action that say on trigger event soooo that when player enters trigger turn bool ON or 1, when player exits trigger turn bool to 0. THEN you need another FSM that is checking to see if both buttons are set to 1 = open door.
Advice: take a look at all the actions carefully because you will see that there are always better ways to do something!
2. For this you need to set both characters into the same layer, then in the physics tab under the edit menu (i think, I'm not in front of unity) uncheck the layer to collide with itself so there will still be collisions with other objects but not with anything in the players new layer.
Cheers!