The first story of a cesarean cut which caused the mother to survive dates back from the year 1500 A.D. which is a very long time after Caesar's death, however the story is deemed unreliable as the reports were written more than 80 years after that surgery was performed, so the first successful surgery in which the mother survived the operation is most likely later. Historians are (according to the sources I could check) all in agreement that Caesar was NOT born by the cesarean cut, even though this operation was named after him.
When it comes to your claim about Egyptians and brain surgery, I could not find documentation on that, only that brain surgery may be thousands of years old, making it possible the Egyptians could do it. I did find reports about the Incas being able to do this, although it appears that it's only a speculation, and no solid evidence. It is said, however that it being advanced enough to produce really good results is only approx a hundred years old.
Of course when it comes to surgery, it's a very wide area of science, and knowledge about one area of surgery tells us very little about knowledge about the other. So knowledge about brain surgery tells us little to nothing about surgery in which somebody belly has to be cut open. So one area does neither confirm nor rule out any other.