I presume the achievements listed in Xbox 360/PS3 sessions are also available in the PC version. Where do I go to find out which ones I've unlocked and the status of remaining requirements for the others??

I'm pretty sure Origin doesn't have any achievements. One of the few things Origin fails on.

Achievements, Trophies, Assignments, Medals, Ribbons, Awards - Whatever you call them both BF3 / MOHW Origin games have them. Are Crysis 3 Achievements a product of Crysis itself or something provided outside of the game by Xbox 360 / PS3??

This why I love steam. I can be an achievement whore.lol. My brother and I compete on games to see who can get whatever achievements in a game. Right now I'm working on metro 2033.