A few "nitpicks" from me:
1) The Engineer at the beginning of the film, on Earth, who gave himself to spread life throughout the planet - would have been there about 3 BILLION years ago. The headless Engineer on LV-223 died about 2 thousand years ago, according to Shaw. Looked identical to the 3 BILLION year old Engineer at the beginning of the film. What species never changes, over BILLIONS of years?!
One that engineers life themselves, or was designed that way by their creator. They have clearly harnessed how to do this. The Engineer from the beginning of the film was also very different from the ones we see on LV-233. They had developed a biomechanoid skin that is blended into their flesh, something the self sacrificing Engineer did not have.
Also, there is no frame of reference for time here. This may a been 200-300,000 years ago for all we know.
2) The c-section scene was not anatomically possible, even within the "science" of the film. The unit cut through Shaw's skin and subcutaneous tissue, and then reached in and pulled out a placenta, the squid was delivered, the unit closed Shaw's skin with staples and she ran off. Well, I've done c-sections in my training, and you simply can't do it this way. Not even close. You have to open the midline muscle tendon, called the linea alba, then mobilize and open the uterus itself (a LARGE muscular organ at this point)" before you can get to the "baby". These layers also have to be closed carefully, one at a time. And no matter HOW much narcotic you have in your system, you can't pull on a spacesuit an hour later, run out of an alien spacecraft, run away from the same spacecraft within the hour as it crashes and rolls toward you, then climb back into the crashed spaceship and pull an android body and head out of the wreckage.
If you went 80 years into the past and showed a doctor a film of a modern day anesthesia and a c-section, he would probably say the same thing. Prometheus is 80 years into the future. Medicine advances exponentially. Note that in the scene just prior to her suiting up where she takes a hand full of pills, the camera pans down and we see the incision is already almost healed. Assume one of those numerous injections was some type of drug that promotes advance tissue regeneration and others some advanced pain killers. It's called science-fiction for a reason

, and they did go out of their way in practically every scene after this to show her in extreme pain, and constantly doubling over.
As far as the timeline I think you may be a bit off. Based on the elapsed time and dates given in the film, the ship arrived in December 23rd. Shaw's squid removal was most likely on the second day, the 25th, Christmas. She packed up and left LV-223 on New Years day, 7 days later.
3) Speaking of which, how in the world was David's head(and body) in the same position on the map room floor, AFTER the shipped took off, then crashed? How was he still "alive" and functioning, after a freaking spaceship crash?
This is interesting, as it is the third or fourth time someone has said this. In the first scene of David post crash, he is talking to Shaw via the remote radio link. His head is nowhere near where it was prior to the crash. When Shaw returns to the Engineer ship to talk to David, you can clearly see his head is in a completely different part of the room, and the place is in shambles, tilted, lights blinking on and off, and neither his body, or Weylands body, which was right beside him prior to the crash, is anywhere to be seen. Nothing is in the same place.
4)
But as the movie goes, now we have proto-xenomorph emerging from an Engineer, on a dead planet. And.... what? What does baby xenomorph do next? Everyone is dead. No food supply. He'll die, too. Never make it to LV 426, never reproduce, never give rise to Xenomorph proper. So what was the point of this scene, really?
I absolutely hate that scene, and felt it was tacked on. If you watched close, there was a mural in the ampule room that showed the entire life cycle of the xeno, from egg, to face hugger, to adult, with an altar below it. The xeno already existed 2000 years prior to the daffy duck xeno birth at the end of Prometheus, and was apparently worshipped.