Does a lot of exercise delay your period?

It can. Short answer: yes. Very common in female marathon runners and other high level athletes. It is thought to be the reaction of the body to prolonged physical stress. Significant mental stress can also change your cycle.
Yes. We see this in young gymnasts , dancers and competitive athletes. It is a sign there is not enough estrogen in your system. Also be aware that when you lack a period from exercise, you are reducing your bone mass as well. Osteoporosis can be a result.
Possibly. A dramatic change in exercise level can temporarily interfere with ovulation and cause a disruption in the regularity of the cycle. Prolonged exercise that results in low body fat (marathoners, gymnasts, etc) may actually see a stoppage of periods for a while. This can result in low estrogen levels that may increase the risk for osteoporosis.