How is it not working exactly? Does the popup no longer appear once you log in, or does it appear and there's no way to claim the reward? Are you still getting items added to your account without the UI interaction (so it's just a UI issue), or are you not receiving any rewards whatsoever?

OK, the whole UI is working fine, everything is working fine. All graphics, all tables, all buttons... EXCEPT, the updating of PROGRESS in completing daily quests, is not working anymore. SO, I have there all daily quests with progress 0 out of X, even when I do things, that should count as progress. (doing that daily quests).

This may sound like a dumb question, but need to rule out the possiblility... are you trying to complete quests in a Solo match instead of in Casual or Ranked?

Reason I ask is that the first set of quests you get following the Tutorial can be completed anywhere, but then the quests from then on require you to have a human opponent. They won't progress if you're just fighting against AI.

Oh, I am sorry, I missed this note.
So anyway - Thanks for help!

You're welcome!

Requring human opponents for quests isn't communicated to the player that well, so no worries - it's a very easy mistake to make. :)