Question: Why didn't he use his crazy super intelligence, or his telekinesis, to either find a cure for his tumor or at the very least slide the tumor out of his own brain?
Answer: George saw the alien light flash twice. The implication was that the first alien light flash actually created the "tumor" in George's brain, and it was the tumor that gave him his superhuman abilities. There's no way George could telekinetically remove the tumor or send it into remission because it was the source of his powers. If he started tampering with it, he would instantly lose his powers.
Ah yes.
Answer: 1. After losing consciousness a second time, George wakes up in the hospital and is told by Dr. Brunder that instead of the tumor destroying brain function, it has been stimulating it not only making George hallucinate seeing a bright light, but, was also responsible for giving him his abilities. Unfortunately, by the time the tumor was detected, it had grown out of control meaning that George had only a short time to live making a search for a cure impossible, especially since he was told there was a very slim chance of survival if he had it removed. 2. If George had tried to use telekinesis to remove the tumor, he would probably have ended up killing himself in the process.