There is no connection between thalassemia and leukemia. Thalassemia is strictly a genetic disorder which is caused by defective hemoglobin genes. The exact causes of leukemia are not certain, but it appears to be a combination of genetic and environmental factors, with an apparent connection between the chemical benzene (found in gasoline and cigarette smoke), and leukemia.
Because thal is a genetic disorder, the gene is something you are born with and carry your entire life. No one gets thal, they are born with it, and they will always have it. Minor does not become intermedia, but intermedia can be re-classified as major if regular transfusions are required. Intermedia would most likely have manifested with an Hb in the 6-8 range by your son's age. Minor can vary greatly as far as symptoms experienced but transfusions are normally never required, except occasionally during thal minor women pregnancies.
Bruising and nosebleeds can be related to low platelets or a vitamin C deficiency. Vitamin C can be safely taken by thal minors, so this should be tried if bruising occurs easily. I am not thal but if I skip my vitamin C supplements, I bruise very easily. Thals are almost universally deficient in C but any thal with an iron absorption problem should not take much C because it helps even more iron to be absorbed. Minors normally don't have excess iron absorption. Nose bleeds are also just part of growing up so unless they become too regular, there is usually nothing to worry about.