Vacuum-air-tight is pretty much out, maybe except some uncraftable vehicles that stop being such after you tinker with them more than just a tiny bit.
For weird atmosphere at good pressure, it would be doable, as long as you don’t mind extra weight slowing you down (possibly being countered by gravity weirdness).
Getting them through portal would probably require variable size portals, or more likely an area teleport as opposed to portal you drive through.
I think I've suggested this before: Stick the extra dimension on the top few layers of the map - nobody will notice and it'll make a lot of things easier.
Huge “NO” here. This would instantly fling us into an age of wonkery, where monsters, items and vehicles would randomly fall from the sky, coordinate system reports NPCs walking over the sky and skyscrappers have their roofs in the alien dimensions.
Sky IS the limit.
