I would describe roleplaying as more like writing a story with the input of other people than actually pretending to be your characters, if that makes sense? A character's personality is really just how they interact with the world and people around them, so when you're writing from their point of view, it's just trying to look at that personality and figuring out how they would react to things while applying whatever vibe they may have to whatever is they do.
For example, a character who's obsessed with justice would probably try to wrestle a knife out of a murderer's hands; meanwhile, a character who's lazy and uncaring would just watch. if the character who's obsessed with justice is also crude and an asshole, then they'd be cursing out the murderer the whole time they did it; if the character who's lazy and uncaring was polite and sweet, then they would fold their hands in their lap and continue the conversation they were having while someone was getting stabbed to death in the back. If you want to add a little bit more complexity, if the character who cares about justice cared about the law, then they might call the police on the murderer and not get involved; meanwhile, the lazy character would talk to the police when they arrive because it didn't mean they had to go out of their way to do anything, but they would refuse to go to the trial as a witness because they don't want to leave their house. Personalities.
I get attached to characters in my stories while I play them. If I didn't want to see how their story goes, then I wouldn't have any interest in what I'm doing at all -- I usually tend to make a new character for every roleplay I'm in, however, so I forget about most of them after a while. I reuse some of mine if I don't get to use one or I get super attached to some. A lot of people reuse characters because they're attached to every OC they make, and that's good, too. It really depends on what kind of writer you are.
In group roleplays, the plot is usually set by the creator of it and then other people drive it along by piping in ideas about how the plot could progress, little events that could happen (natural disasters, a new villain, etc.) or character-driven things (a character betrays the group, romance, etc. etc.). There are also roleplays where the plot is built from the ground-up by the roleplayers, in which case it usually begins with an inkling (medieval setting, what the conflict might be, etc.) and then others pipe in more ideas for the setting and conflict and whatever until they've got a whole world and plot. Some people just come up with the inkling and then improvise on the rest as they go along, which is also okay. Depends on what your style is.
A bit of a long response, but I hope that helps (and that it wasn't too confusing!).