"Bacteria and viruses can be problems for insects; some insects also face threats from parasitic wasps or other parasites. Insects, however, have very effective immune systems for fighting illness. For instance, when bacteria entering through a wound, insect blood cells are quickly mobilized to surround and digest (phagocytose) the invading bacteria. At the same time, the fat body--a tissue analogous to the mammalian liver--produces large quantities of antibacterial proteins. This immune response of insects is very similar to that in mammals, and in recent years scientists have studied the common fruitfly, Drosophila melanogaster, to learn about fundamentals of immunity in both insects and mammals.
"As for curing a sick insect, they could be treated with antibiotics just as we are. In principle, gene therapy could be used to treat some insect illnesses that have a genetic basis, rather than being caused by an infection. A fruit fly (or any kind of insect) might suffer mutations in certain critical genes--tumor suppressor genes, for example. If tumors developed as the result of the mutation, then one could add a normal copy of that gene to the fly, or at least to its progenitors. Such gene therapy could stop the formation of tumors.
"These answers derive not from specific work on treating sick insects, but rather from basic research on infectious disease, gene transfer and molecular genetics. In reality, most studies have focused on getting rid of insects that are pests, especially for agriculture. Nonetheless, a complete answer to your two questions would also tell us a great deal about our own illnesses and methods for cures as well as understanding insects.