Only general info is here, okay? I am not a physician and I don't work with this type of patient in a nutrition setting...
Thalassemia is a genetic problem in forming "globin" proteins (as in hemoglobin) and thus a microctyic (small red cell) anemia can result. Yes, anemia = poorer oxygen tranport to working muscles. I think existing red cells are more fragile, so heavy training may be contraindicated. You'll need to check with an MD about the particular patient.
The "minor" type is heterozygous and less severe, not usually requiring blood transfusions IIRC. Bilirubin gall stones could occur though. The iron overload comes from blood transfusions and increased absorption of dietary iron as the body attempts to correct its "deficiency", I believe. (Sorry, you'll have to check on this.) Iron chelation therapy is used to reduce iron overload in the Major type of Thalassemia because it is harmful over time (oxidative stress, cell damage and ultimately liver damage). Along these lines, extra vitamin E or certain other antioxidants (phenols from tea, etc.)may help with iron-induced pro-oxidation - but a doctor should be consulted. Vitamin C could worsen the overload by further enhancing iron uptake but it depends on the situation.
Hope this is at least someinformation to consider.