LW#1: Your question: "Can I take a lover as, for the past decade, I have been the caretaker for my husband, who suffered brain damage that has left him a perpetual 11-y-o?" My answer: Yes.
You are doing your duty to him and your children by taking care of him. Even your shrink says you need a break. You need to do your duty for yourself. And it is possible to be a good wife and mother who seeks relief and affection when she can't get it from her husband.
The one caveat I'd throw out there is what happens if you find someone you really click with? And if both of you want to pursue something more? This is obviously a longshot/distant kind of thing, but while you still have the freedom to, chew that over.
LW#2: What. A. Bitch. You act as a surrogate, put on weight, and all the sudden she's telling you what you should or should not eat?
It's possible that bitch is just crazy and has some twisted stuff in her head about femininity, fecundity and needing to feel like some sort of winner when nature has shown that she has rocky soil where no seed can find purchase. That is, she feels "less than" you and has to make up for it. But the thing is, this is not what adults do, and is not behavior you should have to put up with.
That said, when the next opportunity arises, you need to have a talk with her alone. (Maybe you can suggest she go swimsuit shopping with you? You know, to give her an obvious opening?) Although maintaining a level, non-angry approach is the way to go, it will be hard, but I think starting with, "When you make comments about my weight, I feel like you're disrespecting me, and you don't appreciate that it was gained by having your child," is a good way to go.
Whatever excuses she makes, or, worse, if she continues to point out flaws, from here on out your tact is, "My body and what I do with it is my business, and if you make cruel remarks about me, you estrange yourself from me. Is that your intention?" If she has any self-awareness, she might realize that this is what she's been doing all along. But let's not give her that benefit of the doubt. She's going to say no. And you're going to say, "Great. Going forward, I expect no more negative commentary about my body."
See, you're allowed to set the boundary for yourself, and you're not allowed to throw her infertility in her face, either ("I worry what you'll tell your daughter about her body" also is uncalled for, though I'm thinking it). That will just estrange you from her.
LW#3: Can't you shift "Rick" into another department? Have a talk with the other staffers (you've vacationed with) one-on-one about handling his more egregious personality issues (as in, ignore gossip and drama)?
LW#4: Geez, you sound like a buzzkill. No hotdogs and hamburgers? For your kid? I mean, this doesn't sound like an allergy issue, just a control issue.
Can't you people take turns for the responsibility of dinner? Can't you go out to eat a couple of nights?
Can't you be an adult about this and not be controlling?