There are still a lot of people who use "whom," which, strictly speaking, is the preferred English here.
So, жениться is to marry a woman kinda "to wife yourself", выйти замуж is to marry a man, kinda "go for husband". As for gender-neutral variants there are some, but they are a bit less common: Сыграть свадьбу, basically "to play a wedding"; "Ivan and Мария сыграли свадьбу", "Ivan сыграл свадьбу with Maria". There is пожениться, which means "to get themselves married", "Ivan and Maria поженились." Another one is really formal formal: "сочетаться браком" - "to conjoin _selves with marriage" или "сочетаться узами брака" - "conjoin _selves with bonds of marriage"
No. Your sentence is wrong anyway. "Who wants to marry your brother" would be "Кто хочет жениться НА твоем брате" or "Кто хочет выйти замуж ЗА твоего брата".
I think that switches the subject and the object - "Who wants to marry your brother?"
Is жениться implying the brother wants to marry a woman? If so, how can we say this without implying any gender (if at all possible)?