Touhou Project doujins give characters so many different personalities. Due to me not knowing anything about said series, I take em in as if it's their own little thing (i.e. not taking into account it is based on anything).
Do these characters actually have personalities? (As in Touhou Project itself)
Well, you can assume their real personalities from the dialogue the games, or if you read canon doujins and books. A lot of them hold information which might help you understand them a bit more.