The not so short bio: See this. There's a lot of information in there.
Obi-Wan is not actually all that serene. He has a temper. He is impulsive. He is emotional. He has a lot of history that very closely mirror's Anakin's - from love getting him into trouble, to nearly not being taken as a Padwan, to being arrogant and impulsive. He even left the Jedi for a while.
He gets, as he gets older, better at controlling those things. He is never, IMO, perfect. Just better than he used to be.
His default is likely to be after Anakin's fall (ie: when Jedi that have not been slaughtered and are in hiding) but before the original Trilogy. It gives him a better scope of interaction (including 21st century earth, fortunately.), though much less grounding and a lot of angst. It's also very quickly turned him very AU - but hey, that's what RP's about.
Fourth-Wall and Explanation Stuff:
Obi-Wan is being played primarily at a time period where Jedi are mostly extinct and in hiding - he's likely to at least initially introduce himself as 'Ben'. Which should save trouble.
However, I understand entirely that Star Wars is a part of culture for many muses. Anything with a sci-fi or fantasy twist should be fairly easy for it to be explained away, especially in a multi-verse setting.
It happened a really long time ago, in another, far away galaxy. Legends and myth often have their roots in truth. Some time travel and universe (galaxy) moving and you've got an explanation.