Not only did he have to do all you mention, but there was one other thing that I had not heard before, that was mentioned in the History Channel program.
I didn't realize that the rifle supposedly used by Oswald was found hidden behind some boxes on the opposite from the windows, so he had to also hide that rifle and then race down those stairs, all in 78 seconds apparently. How could he have done all that and still not be out of breath, as was reported by someone who saw him at that time?
Another interesting tidbit, the rifle which was found a short time after the shooting didn't test positive for Oswald's fingerprints until 3 days later, after his death, despite being tested for prints before that.