As far as the Iron sulphate tablets are concerned, its difficult to give a hard and fast answer as to how long the treatment may take, since it is dependant upon the severity of the anaemia and the underlying cause (was it dietary, due to excessive blood loss etc, and has the cause been identified and corrected)
Typically, the treatment would be 3 200mg tablets per day, with a repeat blood test after around 2 weeks to see how you are responding. Once the Haemoglobin level has normalised, the therapy is usually continued for around 3 months.
The anaemia itself shouldnt have any effect on your ability to conceive.
Your body is obviously still adjusting to coming off the contraceptive pill, and your periods will normalise, but the length of time this takes will vary from individual to individual. The anaemia and treatment should have no effect on your cycle.
Side effects of Iron therapy can be uncomfortable, ranging from nausea and vomiting, to constipation.