Does not eating and exercise make your period start early?

Answer 1

No, if anything the opposite is true.

You only menstruate if you ovulate, and you only ovulate if your body is physically healthy enough to cope with pregnancy - if a woman was to exercise too much or starve herself then the body will try to prevent pregnancy by preventing or delaying ovulation, thus they would either miss a period or experience a late period.

Thus why girls who suffer from eating disorders like anorexia, or professional athletes, often loose their periods and can lose their ability to have children permanently.