OUT OF CHARACTER
Backtagging: Absolutely! I work full-time and am the slowest tagger ever to tag during the week, so backtagging is definitely a good thing.
Threadjacking/threadhopping: Sure! If it makes sense, go for it.
Fourthwalling: You can give it a shot, but honestly, Gau probably won't understand it. If you're not making any sense to him, he'll just get bored and start fidgeting.
ACTION
Fighting: Friendly roughhousing and play-fighting is fine, but if it comes to an actual battle, we should probably talk things over first because of the Rage attacks.
Injuries: Ask first?
Killing: See above. I'm kind of leery about this, but if it makes sense IC'ly, then maybe.
Telepathy/mind-reading: Go right ahead. You're going to get an endless stream of 'food meat animals play friends thou shiny things' though. Gau's mind is a pretty simple place.
RELATIONS
Hugging: Gau will be confused as hell, but go for it if you like!
Flirting: Any flirting will go WHOOSH right over his head. You're welcome to try, but don't expect Gau to understand or reciprocate. I'm pretty sure his hormones haven't kicked in yet.
Kissing and/or other intimate actions: See above, and please keep in mind that Gau is 13 :\ This goes without saying, but keep it appropriate and please don't be skeevy.