For the Discerning the Transmundane quest.

Yes, technically it obviously should, but it's possible that the action "harvest blood" is only available when you activate a regular Falmer's body.

I don't believe so since he'd probably be listed under Snow Elf not Falmer in the files.

I could be wrong.

Yeah, I'm sure it doesn't though since the Snow Elf race is added through dlc. Game-play mechanics.