Well, source on how they started comes from the http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-twenty-four.
They're much jollier then the Ordinators (not a difficult feat really) and directly serve under Vivec. IIRC, they pool a lot of their numbers from House Redoran, who more coincide with Vivecs ideals of adventure and all that. As for their skills...well, there's nothing explicit, but Sneak, Short-Blade, Destruction, Light Armor, and Marksmanship are the classes Major skills in Morrowind, so that sort of gives us a bit of an idea.
Hard to say. They could have been absorbed into the New Temple after Red Year, but given the implication that the Temple may be fractured, they could still be on their own.
You can see in game that they wear chitin or glass armour most of time. The construction kit describes them as something like "samurai-poets", although the only things I can see that they have in common with pop culture samurai is that they're warriors of a sort and have to show certain social standards. To me, they come across as knight errants who are all finesse.
I find House Redoran an odd fit for them given House Redoran's exceptionally solemn reputation, but then that would be a respectable vocation for a Redoran kinsman who wasn't serious enough to gain respect in his own house. I imagine it serves as an outlet for warriors of that nature. Perhaps they're relieved of responsibilities to their clan as well? And that way of life is cool because Vivec endorses it.
Yeah I heard that too. I think it's true. I wouldn't put it past the kinky as hell Vivec.
To be fair, I'm pretty sure the implication that Alma sleeps with members of Her Hands is there as well, if not stated out right. So Vehk is hardly unique in this case me thinks.
This have some creepy connotations for Sotha Sil and the Fabricants, man I miss fabricants.