1. In my opinion, they're not necessary, but they do look cool, the sway bars are advertised to stiffen the ride up, and the springs drop the car about an inch. I don't have one of these cars yet myself but I get to drive them often enough thanks to working at Subaru so I can't say if I'd personally get these for my car yet, although I will be doing the TRD exhaust.
2. They're expensive, but if you like the look, and again, are a Toyota/TRD purist, it's not too bad of a bargain for OEM quality and they're forged as well.
3. No.
4. Yes, the Pioneer AVIC NEX systems will fit in these cars fine with the proper harness and wiring. I'd personally recommend the 8200 or 8201 since they have a capacitive touch screen which, to put it simply, is like a smartphone or tablet in terms of responsiveness and accuracy. The reason I recommend Pioneer is because the stock headunit already is Pioneer so it makes sense that another one would be the most compatible.
You can check this link and put in your car and it'll show you all of what you'll need to fit it properly:
https://www.crutchfield.com/p_130820...C-8200NEX.html