The funny thing is that thanks to the black goo, almost any incarnation of the "egg producer" can exist in Alien now. Egg morphing and egg laying are both legit but just where did David get his eggs from is the question. The way Shaw's body is displayed on the table is how one would dissect a corpse. The lips you see is just the skin pulled back and pinned down to allow clear access to the thorax. I don't think it is meant that the eggs grow inside of her and then her chest opens up like a pair of doors. David uses her organs and tissues in his experiment. In all honesty I don't think David killed Shaw. Story wise it doesn't make sense for that to happen. However once Shaw is dead, her body was just too good to pass up.
Still, taking note that the first movie was called Prometheus, chaining a human to a rock and having them birth out aliens would fit the central horror theme of the movie.
Although... now that I think about it, he might have done the same thing to her that he did to Holloway after perfecting the goo a bit. He did say he tried to make her more than human and she is obviously changed. hmm