Permissions

Backtagging: Always! :3
Threadhopping: Probably fine, but should ask first.
Fourth walling: Go ahead! Shizuo won't believe you though, and if you seem to know too much about his life, he's definitely not going to be happy. You creeper.

Hugging: Would be awkward and probably not well received.
Flirting: Probably wouldn't even notice.
Kissing: Almost definitely a very bad idea.

Fighting: Totally welcome to it, though Shizuo has a reputation back in his world for being the strongest man in the city, ripping up street signs and throwing around vending machines. He's a lot weaker here, but still not a pushover.
Injury: Would like it to be discussed first, though probably fine ^^
Death: Definitely an ask first situation xD