I dunno if anyone else experiences this, but I hear this single "click" noise (almost sounds like it's coming from under the car when turning off the a/c)

It's loud enough to hear with the window down.

I assume it's the compressor, but it seems like it shouldn't be making a clicking noise?

 

Its the A/C clutch....

 

never heard of that? or a click (one single click) noise in any other car?

 

If you hear it when you push the ac button on and off, you're likely hearing the electrical relay. If you hear it intermittently when the car is running with the ac on then it is likely the ac clutch.

It seems like you have a lot of mechanical concerns about your new fit. Why not bring it to the dealer? it has a bumper to bumper warranty.