@Mordep 

Archer C6 v2 is a Onemesh capable router and the hidden SSIDs that you see are part of that feature.

If you want to disable this feature you can do that from the router WebGUI switch button for Onemesh feature.

What you can do about the wireless interference is to switch off Smart Connect feature and use different wireless channels for 2.4 GHz and 5GHz.

You can use an app like inSSIDer to check the wireless interference around you and select different wireless channel for the Archer C6.

Then you can add your RE330 to extend the Archer C6 wireless coverage.

  @Mordep 

2.4GHz wireless radio flapping is not normal - try using non-overlapping channels like 1,6 or 11 for 2.4GHz band and test the signal strength again.

If this issue persists then you probably have a 2.4Ghz radio issue - try using the 5GHz band, it's quite faster and you can extend it with the RE330.

  @Mordep 

Other than reset the Archer C6 to its factory defaults and if the issue still persists testing with another power supply (12 V ⎓ 1 A) there's nothing you can do more.

By the way, If the router  is under warranty you can claim a replacement from your retailer or contact your local service.