1)Resolution and refresh target?
2)Whether it bottlenecks depends on the games you play. You would indeed run into problems with titles that can use more than 4 threads, which is the max of your current chip.
What you can do to check:
Play your currently 'trending' games on high/ultra settings. Take note of the average, minimum, and max fps.
Then play those games on low. Again, take note of the avg, min, and max.
Does fps go up when settings are lowered? If so, it means your current cpu can handle a stronger gpu.
Does fps stay the same, or changes slightly? Then you would be cpu limited.
3)Unfortunately, 4xxx series I7s can still go for top dollar, even in the used market. Unless you can get a really good deal on one, you'd likely be better off buying a brand new cpu/motherboard/ram combo with how much people are selling those old cpus for.
I don't think I'd pay more than $130-150 for a used I7 4770K or 4790K.