So I tracked down the problem - it was actually wy power supply that was running at unstable coltages and causing general system instability.
For some reason it manifiested in a way that once the Intel HD graphics drivers were installed, the system would randomly reboot.
I'm sorry I doubted you Intel, it wasn't your motherboard.
My problem was with my Corsair F60 SSD with a Sandforce chip.
I've moved to Crucial SSD, and all issues has gone.
If you used an SSD that has already any OS installed (from other motherboard),
then format and install again.
Try to use IDE insdead of AHCI on BIOS for SSD chanel, and make new instalation.
You can read here:
Update your BIOS as well.