Threadhopping with this character - yes/no/it depends? Sure, unless the thread seems private.
Backtagging with this character - yes/no/it depends? Yes. I'm a bit slow, and timezones can be something of a pain, so I'm sure it'll happen.
Back-dating entries with this character - yes/no/it depends? Yes.
Hugging/kissing/other sort of intimate actions with this character? Hawk's okay with physical attention, and a bit of a flirt with the opposite gender. He's fine with attention and might initiate, but he'd be unlikely to take it past a kiss. Groping is not really on his cards.
Punching or causing some other form of physical harm to this character? Sure. I'm not much of a hand with fight scenes, so it'd probably be best to talk about it first.
Is there anything that should not be mentioned near this character? Dead best friends.
Is there anything you need us to know about interacting with this character (i.e. special physical features or abilities)? In Seiken Densetsu 3, there's a process called class change that augments a person's abilities. People can choose either a Light path, which is more focused on healing and defensive abilities, or a Dark path, which is more focused on offensive abilities. Initiating a class change involves travelling to one of the Mana Stones- any of them, not just the Light or Dark Stones (neither of which are accessible at that point in game, anyway). How the process works isn't entirely made clear within the game, but given that it can only happen at the Mana Stones and a statue flowing with the same energy and an item is also required for a second class change, it's my belief that it acts more as a path to draw out part of the person rather than an outside force becoming part of the person.
Hawk has gone through a single class change, taking the Dark path to become a Ninja. He can throw shuriken at an enemy, or perform one of four element-based jutsus to damage an enemy and lower their abilities.
I'm not sure whether Hawk would ping anyone for darkness, given the class change. My feeling is that it would probably be a low-level ping, but I'm happy to talk about it.
Anything else that was not mentioned above? No, not really.