Aw, that's so exciting! I'm amazed by the trainers who keep it up while they are pregnant. Heck, I once took a kickboxing class from a woman who was about eight months pregnant. I'm pretty sure she was from Krypton or something.
For both of these types of questions, I think she should assume that the people are speaking out of good intentions.
For the first, they are of course silly (she's a professional and presumably knows what she's doing), but I'd imagine that they are mostly automatic, like the "Watch out for the car" comments that we sometimes make in parking lots. Simply acknowledging that you've got it under control usually does the trick. I think the idea of simply saying that she's got her doctor's okay is just fine. If she's up for doing a bit more educating (that is her job, after all), I think saying, "Oh, yes, it's fine for me to do squats/inversions/whatever until about month five, but thank you for your concern."
For the second type of question, I'd definitely treat the comments as a compliment. I think it's just a way of people trying to show that they're excited for her. While it's usually not a good idea to mention that someone looks pregnant (just as I don't think it's wise to mention weight gain or loss), if she's mentioned it, I think the comments are most likely supposed to be supportive. I'd see it like complimenting someone on new muscle definition if they've told you that they're trying to tone up.
I think it's pretty cool that you and your trainer talk etiquette.