2. You can call yourself whatever you want.
3. Yes. All the Medical Room indicator means is that you can deploy Bacta Tanks to heal an unconscious/severly wounded person. Bacta Patches, Medikits etc can be used anywhere.
1. Yes it is unusual. Possibly something setup ages ago.
2. Sure. You can deploy you bacta tank in any medical room, doesn't have to be the one you own. However, be aware that anyone can walk up and take it away, and since they are expensive to obtain its best to keep it in a location that you can control the access of. And as I said earlier, any other medical items don;t need a medical room to work in.