My solution in the past was to award a small number of points for asking a question.
As for preventing a single player from holding up the game...yes a 1-day time limit on questions is good. Also, if the person choosing the category does not choose one within one day, the board is open for anyone to pick a category.
How does that sound? There is no need for PMs / e-mails, as the person asking questions will keep changing.