this is supposedly in mining altcoin thread section, you may transfer your question to that location however I gladly help you with some knowledge I have.
1.) What could be the reason I get so low mhs ?
try to overclock/underclock hashrates can achieve higher by playing those clocks, try also to tweak your miner ex. Claymore intensities
2.) Did I make mistake buying Gigabyte, though it has Hynix memory.
no, I think it is not that matter
2.a) If I did mistake with Gigabyte, what brand would you recommend me?
same with number 2 above
3.) Could you recommend any clock rates / bios that might boost a little the mhs?
this is a great read for 1060 clocks and hasrates -
https://bitcointalk.org/index.php?topic=1575547.0and this for 1070 -
https://bitcointalk.org/index.php?topic=2054800.0 4.) Could it be the Driver problem?
possible, however after you read and applied other 1060/1070 users clocks, you have now an idea what adjustment you could do.