It seems that Biter Rammer can be completed if a nest dies while you're inside a vehicle. I shot one to death with my car's gun to prepare the area for ramming and got completion credit.

This one I was aware of for a while. I have to look into what separates the impact (physical) damage type from the bullet (physical) damage type. They're treated as the same thing under the hood, but there might be some kind of subcategory or whatever. Thanks!

I can see why this might be hard to distinguish. It's the same damage type from the same entity from the same force. Still, it's really not a major issue, and worst case you could just reflavor it as a general vehicle achievement.
I assume it does not trigger from tanks and needs a car specifically?

It works from a tank as well.