Yes that is your serving. You are better off getting a variety of protein over your meals because different protein sources have different benefits, but I've been known to eat 4 eggs at multiple meals in a day when I'm pressed for time. I don't know the answer on 2 palm-sized portions of eggs. Because eggs have a higher fat content they are quite filling...when I eat them I generally don't need more than 4 but if I eat chicken I often need 1.5-2 palm sized portions. Good questions maybe another mod will chime in too.
Well you are allowed to have 2 servings of protein if you need it. This would be a question for the top dogs in all seriousness. I'd be scared I'd drop one of my very expensive pastured eggs trying to build a pyramid. And my floors are not really clean right now...and I would scoop it up and eat it anyway.