Position applied for: Patrol/Emergency Response (no sector preference – he's happy to go wherever he's needed) and Investigative Team.
Jack would definitely be up for a leadership position if one became available, but he's also quite happy just following orders. Or, you know, mostly following orders until they conflict with his own views on something…
Is your character psychologically fit? Please elaborate: Jack has spent most of his (long) life fulfilling roles similar to this, so he's definitely experienced, even if he does have a tendency to go off and do his own thing if so inspired. But he has an extremely strong sense of responsibility towards those he considers under his protection, and will lay down his life (time and time again, because he can!) to protect them. He doesn't panic easily.
How much of this would the interview team be able to read?: It is impossible to read Jack's mind (reason unknown) so no-one's going to get anything that way. He's also an experienced con-man so he's good at disguising his real intentions. However, neither would be a problem in this case since he would be fairly open and honest at interview. He honestly does want to protect and help people.
What skills/knowledge/powers/experience does your character possess which would be an asset to the position(s) they are applying for? He's immortal, so even if he gets killed, he'll come right back again, usually within minutes. He's also good with a gun (if he can get hold of one) and has experience of a lot of weapons from different eras. He's not too bad in a hand-to-hand fight either. He also has knowledge of tech from a lot of different eras, which may prove useful here.
How competent is your character in his/her skill set?: Jack's a good fighter and, mostly, a decent strategist, although he does have a tendency to just go in guns blazing and hope for the best, but he generally gets the job done. And he will give everything he has to protect people.