With an iron deficiency & a heart rate (resting) of approximately 82 is it safe to start jumping rope for exercise/getting fit? harmful or beneficial?

Listen to your body: If you do a gentle pretend jump roping, like skipping rope, slowly, you will get good movement that will stimulate blood flow in even 30 seconds. That should increase circulation to your entire body. Doing this every 30 minutes while awake and gradually increasing the duration will be very beneficial to you as you are correcting your iron deficiency. In less than a month you will be stronger.