Position applied for: Patrol, any sector. He's fine with being a leader or not, although either way he may not be terribly quick to call for help in situations he thinks he can handle.
Is your character psychologically fit? Please elaborate: To do patrol work? Definitely. Terry is about as mature about these kinds of duties as it's possible for a high schooler to be, and since he doesn't have a double life to lead and the crime rate (at least in terms of crimes the DF would care about) is probably better here than in Gotham, he oughta be able to actually be relatively relaxed. And there's teammates. Which is probably the part he's least psychologically suited to. He's willing to work with a team, and he'll be pretty friendly with them, but he has this notion that he should be self-reliant whenever possible jammed into his head.
How much of this would the interview team be able to read?: Most to all of it. He has some experience and a little training resisting interrogation (mostly by being coy/smug/a wiseass) but he's willing to be upfront about just about everything, with the exception of a few details that he thinks could lead back to Bruce or his friends.
What skills/knowledge/powers/experience does your character possess which would be an asset to the position(s) they are applying for? Terry is strong, agile, and perceptive. He's got a few years of experience being Batman, which can largely be applied here. He's got decent stealth skills, though he's used to relying on tech he no longer has in that department so there may be a few hiccups. He’s a skilled fighter and athlete, and as Kitty pointed out boomerangs, his weapon of choice, are pretty easy to make. He’s sharp, suspicious and familiar with criminal investigative methods both legal and not.
How competent is your character in his/her skill set?: Pretty competent. Terry still makes the occasional mistake on accounta being a teenager and human, but he's cool under pressure and pretty experienced. He's not really a full-fledged Batman yet, but he's getting there.
Would you like to play out the interview?: Open to it, but not needed