I'm facing the same issues, also the max training level one is not working for me either.
I have 1 out of 3 for the air package one. I managed to get an IFV with the jet, got 2 kills and it only counted 1. Maybe the challenge is miswritten and it actually means to destory 3 enemy IFV/trucks. But I don't know for sure. I have 1 out of 3 though so it tracked something.
The squad deathmatch one is really unfair, I think a rework that would be great is, if any squad member gets a squad wipe, all the whole squad gets the pop up.
Edit: I can't get the heist one either because the final match is never heist...
