Why does Wilson believe Gatsby killed Myrtle in The Great Gatsby?

Tom makes certain that Wilson believes Gatsby was driving the car which killed Myrtle.

Earlier, Wilson had admired Gatsby's yellow Rolls-Royce when Tom stopped by his station for gas. Wilson was already upset, telling Tom that he had to get away and head west with his wife. He vaguely alluded to having learned some information that made a quick departure necessary.

Daisy is actually driving Gatsby's car home when it hits Myrtle. Daisy flees the scene, and Tom and Nick find the aftermath moments later. When Tom realizes who has been killed and a witness verifies that a yellow car had hit Myrtle, he quickly realizes that he needs to protect himself. He pointedly tells Wilson, "That yellow car I was driving this afternoon wasn’t mine—do you hear? I haven’t seen it all afternoon." Particularly because of his own involvement with Myrtle, Tom doesn't want to be associated with the car which killed her.

In his grief, Wilson is determined to find out who the driver of that car was. He recalls how his wife had come home from the city with bruises she couldn't explain about three months prior and suddenly announces that he knows how he can find out who owns the car.

Wilson shows up at Tom's door; Tom and Daisy are already packing for a getaway. Wilson demands that Tom speak with him; his hand rests on a pistol. It doesn't take much convincing for Tom to tell Wilson that Gatsby had killed Myrtle; by doing so, he saves himself from further suspicion and saves his wife from criminal charges.

As Tom later relates these details to Nick, he says that Gatsby "had it coming to him," anyway. Although Nick knows the truth, Tom repeats his lie:

He ran over Myrtle like you’d run over a dog and never even stopped his car.

Nick realizes that trying to reason with Tom is like trying to reason with a child. Tom and Daisy are "careless people" who leave a path of destruction behind them.

There are two important points when considering your question:  what Wilson observes before the event and what Wilson is told after the event.

First let's explore what Wilson observes.  Quite simply, Wilson observes Tom requesting gas for the car he is driving.  Unfortunately for Gatsby, Tom is driving Gatsby's car.  I find it ironic that it isn't Tom that actually wants to stop for gas, ... it's Jordan!

"We've got enough to get us to town," said Tom.
"But there's a garage right there," objected Jordan.  "I don't want to get stalled in this baking heat."

Tom does, however, make the mistake of telling Wilson that the yellow car is Tom's by saying, "How do you like this one? ... I bought it last week."  I think these things cement that there is no premeditated plan to kill Gatsby on Tom's part (in addition to the fact that, of course, he doesn't want Myrtle killed).  At least there's no plan at this point.

When Myrtle is killed and someone sees it's a yellow car that killed her, Tom gets a bit nervous (and puts himself above his grief for a while to appease his selfishness).  He grabs Wilson and tells him that the yellow car wasn't Tom's.  Later, Nick reports that Wilson "announced that he had a way of finding out  who the yellow car belonged to."  Tom said Wilson "was crazy enough to kill me if I hadn't told him who owned the car."

I wouldn't say that Tom "convinced" Wilson. We aren't told that and can't prove that. ...  However, we can safely assume that Tom let Wilson's grief-stricken mind do the work for him.  And you know what?  Tom was happy to do so!

In short, I think it is safe to say that Wilson thinks that Gatsby killed Myrtle because it was Gatsby that owned the yellow "death car," and it was Tom who was glad to share the information.

Why does George Wilson kill Gatsby?

George Wilson is normally a placid man, but long before he kills Gatsby there are signs that he's capable of violence. His physical abuse of his wife Myrtle indicates that he's someone more than willing to resort to violence when things aren't going his way.

When Myrtle is mown down by Gatsby's car, George, despite the numerous tensions in his marriage, is utterly heartbroken. He immediately sets out for revenge against the driver of the car that knocked down and killed his wife.

George is determined to find out who killed his wife. One can sense already that he's not going to go to the police over this matter; he's going to take the law into his own hands. After asking around, George discovers that the yellow car that knocked down and killed Myrtle was the same one driven earlier by Tom. But Tom tells George in front of the police that the car isn't his. In doing so, he's planting the notion in George's mind that the owner of the car was responsible for Myrtle's tragic death. As the car belongs to Gatsby, once George has found out the identity of the car's owner he heads off to Jay's mansion and shoots Gatsby dead, before turning the gun on himself.

Why is it symbolic that Wilson kills Gatsby?

 "A blonde, spiritless man, anemic, and faintly handsome" man, George Wilson, with his pale blue eyes, is a product of the wasteland in which he dwells. He moves listlessly, trapped in his poverty and illusions and eventual hopelessness, outside the sphere of those who enjoy wealth and prosperity, and truly outside of reality. When Myrtle is killed, George cannot even determine who has been his wife's murderer.

Clearly, George Wilson is the counterpoint to Jay Gatsby. His tragedy is the tragedy of Gatsby: they both have loved a woman, who cannot truly give them love; for, she is imagined to be much more than she is. Both men are left with nothing: Wilson's life is meaningless and hopeless, while Gatsby spends the night "watching over nothing" as Daisy and her husband have

...an unmistakable air of natural intimacy about the picture and anybody would have said that they were conspiring together.

Wilson, therefore, represents the defeated spirit of Gatsby. With his pale eyes and ashen dust upon him, he is the shadow of what once has been a vibrant man, the walking symbol of an effete purpose, an effete love, and an effecte American Dream.