Are barracks soldiers allowed to make a request to switch rooms, or get a new roommate?

Yes you can. Ensure that you have a good, valid reason to request this switch.

Absolutely, speak to your first line first and they will relay to your 1SG. Be aware that you’re gonna need a reason more than just “I don’t like the person” or “ I want to be with my friend”

You can submit a request but make sure you have a valid reason or it will likely get denied. It also depends on how much room is in the barracks, etc.