Hi Mik,
Yes, beta zero is either a complete deletion or a mutation that renders the gene useless. I suggest the possibility because his Hb is on the low end of the range for beta minor and also because his HbF is quite high for a minor, which also suggests the possibility of a complete deletion of one beta gene, as there are certain deletions that more or less "make room" for the gamma gene to function, resulting in higher levels of HbF. However, this is not certain as other factors such as hereditary persistence of fetal hemoglobin is sometimes also a factor that explains high HbF levels. I am also a bit confused about one thing. You said iron studies were normal, yet iron has been prescribed when his Hb is low. Unless he is truly iron deficient, iron should never be taken by a thal minor, especially one with a low Hb, as iron can build to harmful levels if taken when not needed, and also with a lower Hb the body naturally compensates by absorbing more iron from the diet, so caution is advised when taking iron.