The reverse is true. Heany cycles is a common cause of iron deficient anemia in women. However, low iron will not cause the irregular cycles. Cycle timing and frequency is hormonally controlled, not influenced per se by iron levels.
No. Your iron level would not affect your cycles, but your cycles could easily affect your iron level.
No. Your irregular periods are hormone-regulated, not by amount of iron in your body. Low blood iron is a result of your excessive blood loss with your periods. You should take supplemental iron pills and get evaluation for your irregular periods, check with your OB/GYN provider.