A GPU can't bottleneck a CPU. You can buy a GTX 980 and that doesn't mean the CPU load will reach 100%. In my opinion the 280X is the more powerful card but it also uses a lot more power. Maybe GTX 960 is worth the money if you overclock it.
No. It will run fine. I will suggest r9 280x instead of gtx 960. It had more VCore and VRAM and more efficiency.
Corsair cx I'd budget series and not really meant for overclocking. Don't overclock GPU with that PSU ....
A GPU can't bottleneck a CPU. You can buy a GTX 980 and that doesn't mean the CPU load will reach 100%. In my opinion the 280X is the more powerful card but it also uses a lot more power. Maybe GTX 960 is worth the money if you overclock it.