1) I don't think this is currently possible - the menu screens are only for using stuff on your own group.
2) You've most likely set up a Tooltip HUD. Either enable No Display in the HUD to not display it, or disable using tooltips in your menu screen.
3) Yes, you can change that by either showing a combatant selection before opening the screen (coming from an overview menu) or using the combatant change keys set up in the menu screen.