@Riley_S 

Thank you, but as I mentioned in my post I have already tried mac cloning and it did not help. 

After trying everything that I mentioned some of the websites started working,  but others are still inaccessible.

This error is very strange and I have never seen anything like this with other routers

  @Riley_S 
Thank you for your replies. Somehow the issue disappeared by itself today and everything reverted back to normal.
For the history (or if the issue appears again):
1)I haven't tried the wired connection
2)Issue persisted on all devices (2 different laptops and 2 different smartphones)
3)Haven't checked the firewall settings on PC (but I assume that it wasn't the problem as previously everything worked fine) and my phone doesn't have a firewall.
4)Network logs (in the browser) were essentialy empty- there were simply no response
5)Curios detail is that when I pinged those websites from windows cmd the pings were fine with 0 package losses.

Hopefully everyting keeps working, but If this issues reappears I will write another reply.

Have a nice day:)