Zoisite has power over memories. His music may have the potential to call forth hidden memories and hidden pasts - or to suppress them and make someone forget. I will pretty much ask case-by-case whether someone is willing, and whether they want it to 'work', when this comes up ICly.
Zoisite's Permissions
OUT OF CHARACTER
Backtagging: Yes, please!
Threadjacking/threadhopping: Yes, please!
Fourthwalling: Yes; with a fair warning in return that it would make him somewhat suspicious and possibly slightly angry.
ACTION
Fighting: Honestly, this almost depends on my mood at the time; ask first and something can probably be planned out.
Injuries: See above; just ask first. If it follows logically ICly, we can figure something out.
Killing: Not an absolute no, but I don't tend to like it a lot, either. So please just definitely discuss it first.
Telepathy/mind-reading: Possible but difficult; he has a strong will and mental abilities of his own. Again, if plot-relevant, it could probably be worked out, so just discuss first.
RELATIONS
Hugging: Really not likely to happen. He isn't the huggy type at all.
Flirting: If by 'flirting' you mean 'stalking', he's great at it! Flirting with him is fine, reaction would vary of course.
Kissing and/or other intimate actions: Really depends. He's more likely to end up going for taking someone to bed than cuddling.