in my opinion, it's as good as certain that you can't pick up a class, nor abilities.
and also in my opinion, it's (highly) unlikely you'll be able to pick up ammo from dead players.
I think you're right, except that you can pick up other weapons, fitting your class.
These picked up weapons will only have the ammo that was actually in the loader (afaik)
And if you run over the same weapon you're carrying, you get the ammo.