I really don't have the time to read this all but I want to take a shot at obi's question anyways. The reason they can't kill the doctor as a baby is because he fought in the time war. The time war is time-locked so no one can travel in or out of it and it's outcome cannot change. So, even if the doctor were to die before fighting the war, he would have to be alive both before and after the war. Therefore, the doctor cannot be killed as a baby.
About the ultimate redo button, I really don't know why he can't except for the possible reasons of some fixed points in time or to avoid messing up some sort of twisted causality.
Finally, regarding the fixed point in time and the doctor cheating death, a fixed point cannot be moved or edited. So, when River attempts to edit it, time begins to collapse. However, all the doctor knows about April 22, 2011 at 5:02 PM is that he has seen from the tesellecta's archives that an astronaut (which he realizes is River) shoots his body. He also knows that he has to be there. So, he realizes that he can go there inside the tesellecta and the conditions are satisfied. What appears to have happened remains unchanged and the doctor was at the place he needed to be. Also, if the doctor were to actually die there, he wouldn't be able to go to the fields of Trenzalore (where the "fall of the eleventh" might even refer to him, the eleventh doctor) and if he never went to the fields of Trenzalore, no one would want to kill him.
Just a final note: The doctor realizes that while he could avoid going to lake Silencio by continuous time travel for the rest of his days, he also knows that the fixed point has to happen so he must go there, in his current incarnation, anyways.