How long does anemia take to be cured?

It depends. It is very important to know what kind of anemia and what causes it. Iron deficiency is one of the main causes but there are others: vitamin b12/folate deficiency, chronic disease like infection or cancer, genetic conditions, certain medications, toxins, etc. Consulting with your doctor or a hematologist for proper testing and diagnosis is a must before starting any treatment.
Depends. It depends on what kind of anemia you have , is it due to blood loss, iron deficiency, anemia of chronic disease, sickle cell anemia, is it due to bone marrow failure, vitamin B12 deficiency; some anemia will never be cured (sickle anemia) due to it's genetic origin; however if it is due to blood lost, it should be corrected immediately when you received a blood transfusion for example.