MEDICAL INFO. Jack doesn't get sick and heals incredibly fast. There's nothing you need to worry about here.
MENTAL INFO. He's got issues with being close to people. Namely... he tends to get people he cares about killed. Don't be offended if he keeps you at arm's length for a while - stick around him long enough and he tends to get attached despite himself. Low-level psychics may not be able to get anything from him - stronger psychics or those with good training can probably get through whatever shields he has.
FOURTH-WALLING. I'd rather you didn't, for the most part.
PHYSICAL CONTACT. Jack is really, really fond of physical contact, and he's more than capable of brushing off anyone he doesn't want touching him (don't worry, he's not going to react violently even if that happens). Go right ahead.
ROMANCE/SEXUAL RELATIONS. It's going to take a lot of CR-building to get there, but I'm okay with anything, and so is Jack. Jack doesn't like labels, but if you want to slap one on him, it would be pansexual. He can be monogamous, but unless it's really important to his current partner, he generally isn't. At all. When it comes to threading sex, I'd prefer to fade-to-black.
INJURE/KILL. Yes. A resounding yes, go ahead. Like I said, he heals quickly, and comes back to life in a few minutes (or hours, if you really do some damage). You will have to deal with Jack being really annoyed when he comes back, but... he's been known to forgive people killing him pretty easily, so it may not be so bad.
DEVICE HACKING. Jack's pretty tech-savvy - you can hack his Junogam, but his wristband will probably alert him to it. Unless your character is a frighteningly competent technological genius, chances are they won't be able to hack his wriststrap - ask first, if you want to, and we'll talk.
ANYTHING ELSE. Just ask! Email, IM, or the comments of this post all work fine.