Cool question. I think one assumption here is that dinosaurs sat on their eggs. They didn’t necessarily do that. Decomposing vegetation is used be some species to provide heat for incubation. More accurately, the bacteria breaking down the vegetation produce heat. If you have a compost pile, you may have noticed how hot it can get. Some birds--like the megapodes (turkey-like birds) of Australia—use this method. Crocodiles also use decomposing plants for heat. Like a gardener with a compost pile, mothers that use this method move the vegetation around to adjust the temperature. It seems likely that dinosaurs used it too.

As for calculating the strength needed to avoid being crushed, I’ll leave that to the engineers. My guess is that it would be pretty tough for the tiny dinosaur to break out of an egg strong enough for a T. Rex to sit on.

It would not have to be thick at all. It's a matter of how quickly they grew. There are some very large animals that grow from very small eggs, and even the very largest plants grow from seeds that weigh less than a gram.