The format you provided kinda makes it a little difficult to answer this. For example, I'm not sure what you mean by identify. Are you asking if I insert myself or my personality into my characters? Or if I just feel like "this is who I'd want to be if I lived in this world"? Also, I'll assume you mean custom characters, and not something like Bioshock's Booker or Marcus from Gears of War.
That said, I'll still give this a go.
1st vs 3rd person is a little weird. I can tell you I played wow in 3rd person, and I felt like a baller troll rogue, but I also did that for almost two years so there was more than the average amount of attachment. Similar thing for Dragon Age: Origin I guess. Less so for DA2. 1st person I can only think of maybe Fallout 3/NV and the Elder Scrolls games. Good amount of self-insertion or w/e you wanna call it there.
My main was my main. My dawg. Alts didn't matter for shit. Alts are soulless. Which also meant I had no qualms about making them female, but my main is always male.
Human vs Non-human - I usually prefer making a human, but if that's not an option for some reason it doesn't really matter as long as I can understand that backstory/lore of the race I'm playing
SP/MMO/Co-op - I can tell you that what I play in co-op pretty much doesn't matter. An example would be Left 4 Dead. I played Zoey pretty much every time just because I didn't care who I played. Can't really think of a custom character co-op, but maybe I'd care more then, like with an mmo.
Depending on the game, a subsequent playthrough can go either way. I can either try and go even deeper into my own character, or make something completely different just to see what happens. The latter usually doesn't go very far though.
As a final thought I just want to say you should really bring in some more rigid definitions for the things you want. For example, I might make a character that's based off of me appearance wise, and I can answer questions "the way I would answer them", but all I'm really doing is making the story play out in a way I would want it to happen in a book or movie. Does that mean I identify more with the character?