Can a sports hernia heal without surgery?

Not if true hernia. The term sports hernia is a controversial one. If you feel a defect in the abdominal wall and a bulge the answer is no. If it is just pain, and tenderness, I would try rest and rehab before sugary is undertaken. There are reports of people with pain and tenderness that do not have a bulging and far surgery they improve, but it wild be my last resort. Surgery could worsen the situation.
Unlikely. Groin sprain may disappear with time, what ever the reason once hernia develops, it will not disappear with out surgery.