Hi Jozef,
My name is Igor, it's a pleasure for me to help others and I'll try to help you.
Please reinstall network and chipset (motherboard) drivers from ASUS support site.
Try to uninstall Avira.
If this will not help, please share new minidumps.
Note, It is not recommended to share a full memory dump, some personal data may be extracted, thou this is not an easy task. Minidumps are enough in most cases.