swftre

No problem. Have fun with your new case.

Well, I'd start by checking all the (internal) cables, mainly power, and see if there's something loose.

It's ok to use only the 4 pin ... the 4pin connector is good for around 200 watts. Your 3200g will consume at most 80-100 watts when gaming, and overclocked.
The 8 pin connector just raises the maximum power that can be given to cpu to around 350w, but your cpu doesn't use that much.

It should work good enough, my Taichi has a similar thing except its an 8 pin + 4 pin and my psu only has an 8 pin, it works, just can’t extreme overclock.

hard to recommend using a power supply with only 4 pins, but it will work.

Of course not, you would violate the law of aesthetics.
On a serious note, yes you can, but as others suggested, remount cpu cooler and change the thermal paste - and if still bad, maybe even consider a new cooler.

that sounds like an unused censor on the mobo. My asrock a320m got 2 of those, thats unused, so in hwmonitor they always sit around 118c (but idunno why). So ignore that part. But about that cpu... did you reapply the thermal paste when u removed the cpu cooler. It might have been old to begin with + u removed and installed it again. 2nd thing to check is if u got the cpu fan plugged in correctly. While it might not be that its still worth to check just to make sure it isnt anything stupid thats causing this. But im still betting on that thermal paste re-apply.

Reapply paste and check cpu fans

Those numbers sound extreme, what about temp at idle?
Have you checked temperatures with another software, to make sure? Are your current fans running loud? Temp sensor could be  broken or maybe thermal compound is not applied correctly on the CPU... but if you really feel the heat and throttling in real use, You might want to underclock the CPU.