Nope, all of that is extremely messed up. I would think it would be self-evident that double-standards, hyper-controlling behaviors, and downright creepiness (thank you emails, really?) would not be ok. And there is much disagreement about veto power, some people like it, some hate it, it's by no means universal.
I've also been in a secondary relationship for three years, and the only thing that you listed that's true for us is no sleepovers, because that's something that the two of them agreed to with each other long ago and it applies to both of them, they don't sleep apart. But actually, he's agreed to let her make an exception to that rule so that she and I can go on a short trip as soon as she feels comfortable leaving her toddler alone for a night, and I've slept over in their bed multiple times.
If you want to read about my situation, I blog at "story of a secondary" in the blog section of the boards.
I also highly recommend the essays on secondary relationships at www.morethantwo.com
You're being treated very poorly, and you don't have to put it up with it.