Manal,
1) No. A rise in HbF does not lower other hemoglobins. The total Hb will rise as more HbF is added to the total. You are getting confused by percentages. Percentages are not volume. They tell you how much of a specific volume of hemoglobin is which type of Hb. The percentage that the other hemoglobins will be is lower because they are now less percent of the total but their volume hasn't changed. The percentage of each type of hemoglobin does not tell you anything at all about the total volume of hemoglobin.
Take a glass of water to represent hemoglobin. If you have one ounce of water and add an ounce of juice (to represent HbF), then 50% of the total is juice, but you only have two ounces. If you take a 9 ounce glass of water and add the same one ounce of juice, the juice content is only 10% of the total of ten ounces, yet each glass contains the exact same amount of juice. The percentage doesn't tell you anything about the total volume. It is the volume of hemoglobin that is added by HbF induction that matters. The percentage that is of total Hb is barely relevant.
2) If you stop giving hydroxyurea, you can't expect it to keep inducing hemoglobin. The Hb will drop unless some other factor has changed. The percentage increase of HbF isn't what matters. It is the total volume of hemoglobin that matters. It would be nice if there was some way to just prime the pump, so to speak, and stimulate the hemoglobin production and stop giving the stimulus, but so far that isn't the case.
3) Hydroxy suppresses bone marrow activity. It is not a very efficient drug from that stand point. If you stop taking it, whatever the state was prior to taking it, should return.
4) HbA2 is made from combining delta and alpha globins. Not much is produced and unlike HbF, there is no point in human life when it is. There isn't anything to turn on as with HbF. A baby in the womb relies totally on HbF and the goal is to stimulate this again to produce enough HbF to compensate for the lack of normal adult hemoglobin (Hb). You are asking the delta gene to do something it has never done at any point in the life of a human, whereas turning the gamma back on is asking to do something that was active when the human was a fetus. It would be unlikely that anything could modify the delta gene enough to make a serious impact on total Hb.