Starships were meant to fly

Hugging: Sure. It may be stiff and awkward if he doesn't know you tho.
Kissing: Definitely.
Flirting: Always.
Fighting: It's all good. (He's probably the one who started it lbr.)
Injuring: Details may need to be discussed but in general, sure.
Killing: Ask first pls.
Telepathy/Mind-reading: Same as above.
Shipping: He's pansexual af so have at. Good with crewmates always, John Harrison/Khan in AU scenarios, and crosscanon (I tend to enjoy AUing Kirk into other canons a lot so it's all good).
(Peter Quill and Poe Dameron are insta-yes ftr.)