1. “He cannot be omnipotent and have free will.”
our all-powerful God can choose between the many good acts that He is capable of doing. He can act or refrain from acting.
2. “He cannot bestow free will upon man to say man has a choice between good and evil, while at the same time not have the ability to choose evil himself.”
God does not choose evil himself, but he makes us truly and fully persons, which means we can exercise our free will for good or evil.
3. “He can’t allow the absence of good if His Goodness is his nature. He wouldn’t allow it.”
Sure He can. He gives us the full responsibility of persons.
These claims by your friend are baseless assertions. He should have to prove his claims, you shouldn't have to prove he is wrong to his satisfaction. He is not in charge of deciding truth.
Roman Catholic theologian