I used to ask loads of questions - where do they work / how long have they worked there / do they like working there. (you need to know this because of the rent). Do they work different hours / shifts from you - if so can you cope with them coming home and possibly being noisy when you are asleep. What sort of music do they like - do they play it loud - will you be sharing the living room and TV - if so what kind of TV programmes do they like. Politics - do they feel strongly about politics / does their political leanings clash with yours. Does he/she have a boy/girlfriend and will they want that person to stay over - if so, how often - if more than one night a week you might want to charge extra for additional gas / electricity. Food - are they/you veggie. Do they have any other dietary requirements. Bathroom arrangements - timing in the mornings and evenings - keeping it tidy. Cleaning - who does what. Shopping - who does what - would any items (loo roll, cleaning stuff) be paid for out of a kitty.
Most important, though, is does the person seem to be the sort who will take criticism okay. There is NOTHING worse than sharing with someone who constantly does something which is incredibly annoying and not being able to say something about it for fear they'll take offence. *Memories of sharing with a bloke who shed more hair than my dogs but never rinsed it off the bath / sink. Yuck.*
Finally..... ALWAYS get a months rent as deposit. I felt sorry for someone once and didn't bother - she
off and left me with a massive phone bill. Oh yes, do ask if they've got friends or relatives who live abroad!