How many phlebotomies will I need to have a normal iron level again?

Depend on severity. Treatment can start from weekly to several weeks till depletion of iron stores is achieved-ferritin level <50mcg/ml and transferrin saturation <30%.
Depends. If it is for genetic hemochromatosis, then weekly phlebotomy is done until anemia develops or the ferritin is around 50. Long term management is to keep a ferritin around 50.