A Detached Hand will "acts as a wizard’s familiar, using your character level as your effective wizard level". Does that mean it can take Familiar archetypes, provided it has the required abilities to replace?
I think only the Elemental archetype is actually available, but a flying, Auran-speaking hand would be... interesting. And since a Detached Hand is posessed by a "ghost, spirit, or outsider", having an air elemental spirit in your pinky matches the fluff.
IMO it should be fine so long as all of the pre-reqs have been met.
While not an option by the RAW, I would think most DMs would be ok with you taking the feat Improved Familiar Bond in order to pick up the missing abilities as well. Thereby making the rest of the archetypes options.
It's similar to the tumor familiar, which can have archetypes, so it should be fine if it qualifies.
Unclear from the FAQ, but if so then yeah, it'd be fine.
Ultimate Wilderness specifically bans the Protector archetype for tumor familiars, but then Ultimate Wilderness has a lot of retroactive changes that shouldn't really have been printed in an optional supplement--even a core one--so unless you're in PFS, it's the GM's call. (And this isn't a tumor familiar anyway, so that's even more wiggle room for table variation.)