A1. If you want to save money, go with the AMD CPU's. If u want to have a CPU that is stronger but is more costly, Intel is the way to go.
A2. Yes, AMD CPU's and Nvidia Gpu's (or the other way around) will definitely work together. I have a FX-8320 with a Gtx 770 and it work perfectly fine. The only problem with this mix match up is that if you decide to go with an AMD CPU, you will have a slower output video signal with your graphics card to your monitor because of AMD motherboards slower pci-express output. (I barely notice the difference)
A3. In my opinion, i would have to go with setup 3 because both nvidia and amd components in the build are good.
A4. No errors, i can think of.