I’ve heard that when Mashiach comes, the b’chorim will do the avodah. However, there is a famous story with the Chofetz Chaim that showed he held that when Mashiach comes, he, as a kohen, will do it. Maybe both will?
As for the C-section question, I asked that to a Rav, as my oldest is a boy who was born via c-section. I was told that all the halachos are the same except for pidyon haben.