Try to keep one of the Garrison-AIs alive (maybe one in a closed tower or small room, where they cant hit you?). That involves some risk, since he COULD step outside and shoot you in the back, but that keeps the outpost as NATO, since you didnt kill all Garrison.

Second option is, to start firing mortars (or other noisy stuff) that makes the enemy to send forces to check that out.

In general, NATO does try to take its outposts back, maybe you get lucky and a random patrol walks in and recaptures it for NATO again, but that depends on the surroundings of the outpost, the terrain, warlevel and so on.

My personal tactic in the beginning is to hit roadblocks and patrols, then move up to hit&runs at outposts, like you. There i clear out all clearly visible targets, then move in for CQB. In my experience, there is always one or two soldiers in little bunkerbuildings or in some tower-room. I just find them, shoot them in the leg with a pistol, then heal them using ACE (use bandages and morphine), then takeaway their guns and stuff when they are still out, once they get up again, they surrender. Then i dont deal with them (aka just leave them hanging) and have 2-3 more minutes to loot some good stuff, and finally get the hell out of there. (Apparently NATO/USAF doesnt like to loose Outposts and some guys with guns show up to tickle you^^)

Interesting, I got like an assault team QRF at war level 1, then at war level 2 I got more than that, like a prowler and some assault teams. And at 3 they sent in Ghost Hawks and paratroopers guys, and last at 4 which I am at now they send Napalm strikes which kill my entire garrison.

How do you minimize losses for the Napalm strikes. I don't have AA capability right now.

Maybe get some AA around you and your troops.
Secondly, find where they are firing from and/or where the helis/jets are stationed and shoot some mortarshells in it. The enemy would then need to actually replace them, if i am not mistaken.

I'd suspect that they send them from the closest airport...

You can't necessarily give it back but certainly don't defend against QRF if you intend to. The type of response do vary quite a bit. If your campaign stretch long enough the opposition will eventually get back the territory via direct attack mission. Sometimes if you grind a region for too long, the opponent's manpower is severely depleted and the response becomes very tepid. If you are solely focused on grinding gear, you can try to leave a few enemy outpost and spawn ammo truck missions from them. Alternatively if the region is too depleted, move to another region on the map and start afresh against stronger garrison. There isn't necessarily a good counter to enemy airpower and I am pretty sure barbolani intended it that way. Sometimes you have to accept setbacks and cede ground.