Do I need an apartment to become a hair stylist? or just a chair and scizzors?
Well you need somewhere to drop the chair to skill. So yes, its best to have an apartment or house, unless you want to go balls to the wall and skill out in the open 
Just be careful, if you ctd, the chair might have been picked up when u log back in
you need somewhere to place the chair, yes I belive so. I dont think you can drop it on ground and cut them there (plus the risk of someone picking it up is always present) since you cant cut people in other peoples chair either!
well i wont be cutting hair after all then