Not sure if I have not read something of the stuff I´m going to write down now has been mentioned before, if so I´m sorry.
Supression:
Someone suggested Points as a reward for supression and although it seems to encourage Teamwork it might also give away the enemys Position, especially if you are using something like a mg, with ist high RoF.
As for effects of beeing supressed I could imagine something like a loud zing noise where the bullet flies past and a sway effect to the other direction. For example if the bullte goes past you on the left your gun would swing to the right a bit.
Medics:
I´m not sure if you posted your respawn System somewhere else before, but I havent seen it, so this might not work. But maybe the medic could set up a first aid Point somewhere ( like Rally Points in PR for example) and if he manages to carry a wounded Soldier to that Point he will get patched up there instead of respawning at the farer away spawn Point. ( though this is futile if spawn on squadleader is planed).
Additional:
I would love to see a giving up Option, I really hate the fact that in games you alway have to kill each and every enemy, while in RL Soldiers surrenderd quite often. Maybe you could implement a slow surrender Animation at whichs end one is spawned at the next Objective (maybe double the respawn time?) but does not loose Tickets. ( So it benefits both sides )
Greetings
Boltaction