Is it possible to switch my head unit?
 

I'm using the 2014 Touring and am not happy with the built-in head unit, so I'm thinking about getting a better looking screen instead.

Thing is, the current head unit itself is connected to few things, such as commands in steering wheel and many others, I'm afraid it might affect the controls and limit my accessibility after all.

If it's totally fine to replace the current head unit, would you recommend me a nice looking screen that offers many features, under $500?

Yes, you can replace the H/U. I'm no expert on compatibility issues, but these folks are:
Crutchfield: Car Stereo, Speakers, Home Theater, Pro Audio, 4k TV