In The Great Gatsby, no, Wilson does not know that Tom is having an affair with his wife. A sister knows, but she keeps the information to herself.
Wilson goes to Tom to ask about the car, and Tom tells him that Gatsby is the owner of the car that hits and kills his wife.
Of course, Wilson isn't aware of quite a few things, the most important of which is that Daisy was actually driving the car when Myrtle was hit.
Tom gets back at Gatsby in two ways, then: he manages to hold on to Daisy, and he also indirectly leads to his death by telling Wilson that Gatsby owns the car that hit his wife.
I do not think that Wilson could possibly have known that Tom was Myrtle's lover.
The major reason I think this is because he never acts in any way suspicious towards Tom. Even when he has Myrtle locked up because he suspects she is cheating on him, he still keeps acting quite normally towards Tom. In fact, he does not even react badly to Tom after Myrtle has been killed. Surely if he knew they were lovers, her death would have made him lose his control and confront Tom.
As far as Tom's information, I think it makes sense that Wilson would believe him. It was Gatsby's car, after all. And it seems more likely that Wilson would believe a man could have done the killing. I think he would not automatically suspect a woman.