The first two pics look like Taurillon Clémence, but maybe a close up picture could help. As a general and approximate rule, you can tell not only because of the way the bag stands by himself, but also because of the slightly flatter grain, becoming even flatter, almost grainless where the leather is more stretched, like on corners and handles.
I am 100% sure that the third picture is Togo. It stands in a different, more rigid way, and also the grain is more "bumpy" and the vertical lines are typical of Togo (even if sometimes you find togo pieces without those vertical veins)
Yes, it is true that some Togo bags end up being more floopy than the usual way we are used to see them stand up, but Taurillon Clémence is going to be even floopier. Your new bag is super gorgeous though, so except if you really are concerned about the floopy factor I would keep it.
For what is regarding thicker handles, yes, this is possible. Birkins are hand made there may be some differences from one piece to another, and on top of that some hides may be slightly thicker. I have personally found such small differences in some of my H bags.
Please also keep in mind that leather is a natural material, there may be some slight differences in the way colour pigments penetrate one hide compared to another of the same leather, and one hide may be softer than another.
Couldn't have said it better.