As for question #2, I honestly wouldn't get pizza around NYP, I've never had a good slice near there and I've lived here for 20 years.
But if you are going to the Museum of Natural History, check out Ray's Pizza on 82nd Street and Columbus for the more "New York style on the go" pizza. Note: All Rays are not the same, so if you see another Ray's randomly in NY, it is likely not as good as this one. If you are looking for more of a sit down meal with higher quality pizza, Patsy's Pizzeria on 74th and Columbus is great but you need to order a pie, not individual slices.
By the way, the Petrosaur exhibit is great! I went with my significant other a few weeks ago. They have expert archaeologists (or whatever the term is for dinosaur researchers... Paleontologists?) that just walk around and talk to folks about the various fossils, I've never seen that in a special exhibit before. I would also recommend not going to the major museums on a weekend if possible. Nothing wrong with weekends, it's just significantly more crowded with tourists.