ESC should always work… gamepad is irrelevant. Which menu is this? The in-mission pause menu? It doesn’t work if you have a gamepad connected?
Added to v.60 
Idea
This is an old account, last active in May 2019, shortly after medals were reset:
Because that space is taken up by “Incoming:”. You can see the waves at the bottom-right anyway
No.
No.
Yes.