1) As you have already an i5, going to i7 with the GTX 970 you wouldn't see any performance gain.
https://www.youtube.com/watch?v=Vvd_leZqSyA
2) That would be the best scenario, for getting higher frame-rates on higher resolutions.
3) That would cost much more than 200-250 bucks. 230 for the CPU plus mobo and memory modules.
But you will use the same GTX 970 GPU. So not much a win here.
If you would built a new PC from scratch, then you could very well go with an GTX 1070 plus an i7 processor. That would be a good much.
Never games most obviously will use those extra threads of that CPU,
and as the CPU is the number one limiting factor on faster GPU's like the GTX 1070, that would make more sense.
An i7 would scale better on very fast GPU's as the test shows below.
https://www.youtube.com/watch?v=EhaB1dqYv_I
(but it depends mostly on the game engine and not all games have a benefit from more threads.)
Even so, on never builds i would recommend an i7 over a i5, if someone can afford it.
It's a more future proof solution, and well...you don't wanna change your processor more than once on the whole lifetime of your RIG.
But you can "mess up" with a better GPU if the time comes...
However, even an i5 will do the trick just fine, in the most cases.
So, your in only concern should be, of getting a faster GPU!