I haven't used any corsair and coolermaster supplies before, but on the forums i have read alot about psu issues with corsair VS series. Coolermaster has always had good products and i have never heard anyone having problems with a coolermaster psu
GPU is the issue, the only thing cpu does is physics and things like drawcalls, when it comes to higher or lower resolutions the gpu is more important. I recommend getting a better gpu as your cpu is still capable.
The fans should blow into the radiator for ultimate performance. To know what side they need to be mounter on you can just keep them like this, start pc, and feel if the fans are blowing into the radiator or not.
If you are going to play the games at native resolution (1440x900 on old and 1920x1080 on the new monotor) then you are going to suffer some frames because your resolution goes up, depending on the game you will lose 5 - 10 frames unless you are going to play 1440x900 on the 1920x1080 monitor...
Might be lack of memory if your mouse locks up like that, but i don't understand why you have the issue with csgo as csgo doesn't use a lot of memory. you might want to check on cpu, memory and gpu usage.
Depends on what games you want to play. Games like battlefield like more cores so an i7 8700k, but you shouldn't get the k version if you aren't going to overclock. For casual games that aren't very cpu demanding a i5 would be the best choice.