@MR2Jedi
I took it to a private repair shop by me who checked it out for free and said that they had no idea why it was vibrating and they couldn't get fast enough because of the weather to see it vibrate. They also said that I needed new shocks in the back and new CV joints in the front. They quoted the following (Parts and Labor):
2 front axles $577 (Warranty covers $485)
2 rear shocks $568
The said that the vibrating should go away after the new axles in the front and an alignment.
Does this sound reasonable? Should I ask them to check the wheel weights?
@Zembonez
I drove drifted and then my friend drifted while I recorded from outside. There's no curbs around and I know I didn't hit a pothole. When my friend was drifting, I heard rapid clicks in the middle and yelled at him to stop so I don't know if that caused anything.
Here's a video of the clicking I heard.