New PC build, general questions.

00. more than enough for anything current.
01. antything with 4+ pipes or any AIO. https://www.gamingscan.com/best-cpu-cooler/
anything from here that fits by look/cash is a lot more than you need.
03. if PCsays ok then you should be fine. sometimes its hard to mount as you have 1cm left to put hand inside....
04.750 vs 650 is not a lot different. Choose a better deal here or higher ranking (bronze, gold, etc) 650 W should work with any single card

00> If you're putting that 8700k on a budget Z370, make sure to include fans around the CPU socket region to provide extra airflow to the MB's VRM or you may not have a system for long.

01> Here's your go to CPU cooler guide, with regard to price-to-performance:
a) Strict budget - > Deepcool GAMMAX 400
b) OK budget - > Scythe Fuma / Mugen 5
c) Want more cooling than (b), your next level up is an CLC/AIO.
The other options really are just for either looks, brand loyalty, specifics limitation imposed by the case size and/or availability in your region.

(a) GAMMAX 400 is solid performance and limited noise so long it doesn't have to run at its max fan speed.
(b) the Fuma is performance oriented, while the Mugen 5 is noise oriented (and better compatibility with tall RAM like the TridentZ RGB in your build).
(c) Compare to the few best, and most expensive, air tower, the Fuma already representing 97-99% their performance. So at the price bracket above the Fuma, unless you really must stick to air tower, you'll be much better served by going to a 240mm All-in-One/Close-loop-liquid-cooler (which is the largest size supported in the Focus G, which would be a fairly tight fit).

03> There's no problem with fitting the STRIX into the Focus G. The STRIX is ~298mm long and the Focus G can support graphic card 380mm long.

04> Unless you're looking at SLI-ing the 1070, you may want to go for a 650W version instead. Your 8700k+1070 are going to draw like 370W and a GTX1080ti-tier upgrade would only increase the power draw by another ~120W.

05> Really depends on what you want to do. But given that the Pascal generation is already 2 years old at this point, I personally don't recommend trying to overspent for "future proofing" because the "future" for the Pascal gen is already here.

06> The Focus G is pretty good for the hardware. It has a mesh front to help facilitate better airflow inside the case for cooling the CPU+GPU and therefore is actually better than a good chunk of more expensive case with closed/solid front. But again, for the usage of the 8700k with that MB, you'll want at least one more 120mm fan for the rear or top mount.

What is the max budget you plan on spending