I agree with most of what you all are saying, but to frank entrepreneurs need make it a part of their regular schedule. Here is a health and fitness video for entrepreneurs I found extremely helpful!
It depends on what exactly you want to do. If you intend to work at your gym as a trainer or nutrition counselor, you'll need to be qualified to do that. This would be kind of like having your own practice as a nutritionist or something, with enhanced facilities for your clients to work in. It would also probably have lower start-up costs since you could start smaller and maybe wouldn't have to hire many employees. However, if you wanted to expand you would eventually need to hire people.
Yeah. This is exactly the "case." Practically all successful entrepreneurs (or millionaires) are also part-time sportsmen and sportswomen. They are the ones to get up at 5 am to go for a run. They eat healthy food and they exercise. This is an astonishing but this is true. Exercise (no matter what kind) should be the beginning of every entrepreneur's day.
I don't necessarily agree that "practically all" successful entrepreneurs are sportsmen, sportswomen, or athletes. Disciplined, yes. Working hard and not eating, maybe. Fit, not necessarily. I'll have to check for some stats about that, if any exist.