I used to have massive problems with my old setup, but thanks to axe0's attention I have fixed it all.
Since then, I've upgraded my rig, and ever since I've got a couple of seemingly random BSOD-s. They seem to happen when PC is left idle. Ie. 30-40 mins of inactivity, I notice my screen light up and a BSOD on the screen. I've also got one or two BSODs when randomly clicking on desktop.
Things I've upgraded: mobo, RAM, PSU. My Win10 install is fresh.
Important note: my Mobo and RAM aren't officially compatible. It's something I didn't notice upon buying the RAM - the mobo doesn't list my RAM as supported. HOWEVER, the RAM was set in BIOS to default values (as on the box) and passed memtest + I've finished a couple games on such setup without any issues or BSODs.
Please take a look and tell me if something needs a bit of tweaking.