Threadhopping with this character?: Absolutely! Just ping me on AIM, PM me, or put up an OOC note on an existing thread to let me know you want in.
Backtagging with this character?: Of course! You want to continue? Be my guest!
Hugging this character?: Ehh. Depends. But mostly no unless you really know him and the circumstances allow. If they don't, you'll most likely get shoved away pretty strongly.
Giving this character a kiss?: Uh...well...uh...Sure? His mouth is too wide for frenching, so the best he can do is the PG-13 version. This is an awesome way to make him flustered beyond belief because, well, who the heck would want to kiss a giant turtle?
(Something more intimate?): WHAT? Okay, just, uh... WHAT? If you make it clear you really want it, then he'll probably be on board. He's...a little desperate. But he also has absolutely no experience in anything besides what he's seen on TV or in magazines. And all that bravado and confidence he puts on about his sexuality will most likely vanish when it's time to get down and dirty. Grabby hands are fine, but performance? Aha...no. I could go on a rant about turtle anatomy, but I won't. Let me just say it's very different from our own, and he knows it.
(Relationships?): If you're into it, he'll probably be into it too.
Punching this character (provided they can fight back): Sure. If it's all in good fun, he'll probably jab you right back. But if you want to start a fight, he'll be more than willing to kick your ass.
(Injury?): Considering Raph's tendency to pick fights even if he's outmatched, injuries happen. Just don't godmod it, please. I'll do my best to judge a realistic consequence for your character's blows, and will probably ping you on AIM or PM your account for details.
(Death?): Depends on the circumstance. I'd need a very good reason.
Is there anything you do not want mentioned near this character?: Eh, he's pretty touchy about a lot of things, but his head isn't made of glass. Say whatever you want. He sure does.
Is there anything you need us to know about interacting with this character?: He's very, very close with his brothers. What you do to one, you do to all. So before you take action, consider the consequences.
Also, a lot of characters around here have the issue of 4th walling him. He's a pretty well-known aspect of pop culture if your character's from modern day America, or even Japan to a degree. So if your character recognizes him from the cartoon or whatever back at home, go right ahead and break his brain.
Lastly, do not taunt/tease/disrespect him unless you want a fight. He is very emotionally sensitive, but not in the typical "boo-hoo you hurt my feelings" way. Instead, he takes everything as a threat, and will get freakin' mad as hell if you carry it out beyond his warnings. He will start fights over stupid stuff like this, so don't expect him to let things roll off his shoulders. They won't, and if you push him too hard, it will end in violence.
An exception to this is his family and friends. If you believe you fall under Raph's immediate circle of protection: i.e. he talks to you more openly than most, and seems overall happy to be around you, you'll probably be able to get away with most anything. If you smack him, he'll laugh it off or jab you back good-naturedly. If you tease him, he'll laugh and tease you back. If you want to fight, be it physically or verbally, it'll be much harder to invoke a violent response from him than most people.
But beware. This status is hard-earned. Raph is not the type to trust people, and he generally will hate you first and get to know you later.