Yes they are allowed - I just checked the rule book and can't see a maximum length, it just says they must not be of a length that disturbs other riders.
You're allowed schooling/dressage whips at prelim level for BD, except for championships. I think the maximum length rule has been abolished, so any length is fine!
it depends if you are riding at a PC event or a riding club event. if you are then its 110cm, if not then unaffliated comps are run under BD rules which are whatever length you like as long as it doset interfear with other riders when you are warming up.