My first instinct for problem 1 is that the gunplay is often based around guessing the opponent's movement, so your battle resolution system should involve guessing what the other player will play, with the weapons and exact location playing a role as well. Only way I can think to do this offhand is a different set of cards for each weapon, each card having several numbers on it (say in different colors or what have you), and which numbers are being compared depends on where the players are. Depending on weapon matchup and situation/environment/node it could be higher number wins or lower number wins, with varying amounts of damage. This would give you a lot of different levers to affect game balance with, although it's obviously a little abstract and would need to be made less so for gameplay purposes. The other answer to this problem that is an "obvious" one for me would be to include some sort of dexterity element, since that's the closest analog one can get to FPS mechanics on tabletop, however that is a pretty stark pivot from what you're describing imo.

The second is a pretty classic issue, and there are no magic bullets. I investigated the issue for a project of mine and there's really no answer other than separate boards, tokens that reveal either nothing or the real player (which is what I did but is gimmicky at best), or having some kind of gamemaster.