1. at least three posts a week, preferably in the main section, but also in the other sections, if that's where the person is
i don't really fully understand the activity stuff so that's as much as i understand
2. queens ? probably not, however, i don't know for sure, definitely not for med cats, but probably not for deputies either, since they're caring for kits
3. no, as it's not something required for the deputy, it's up to what the roleplayer of the picker wants their deputy to be like, if they want their deputy to have an apprentice, then that might be a requirement, but if it doesn't matter, it won't be a requirement
some additional info :
when picking, previous strikes might be taken into account, depending on how many, and how recently they received the strike
it might also be taken into account how friendly they are to users
also bellyaching, that isn't a good way to get a highrank at all, as it will most likely have the person ignore your form/character
i hope this helped !