For a while now, my chat notification has been alerting me of a new message but I have read it already and cleared it from my chat window yet the notification is still up. I cleared all previous chat conversations earlier and the notification never went away and it has been like this for months. There seems to be problem with my avatar not showing the new one I switched to in forums in both old and newer posts I've made.

Not sure about the chat (people have been complaining about this happeneing; one possible reason could be that you've been contacted by a scammer, who's since been banned), but for the avatar just wait it out. Usually no more than 24 hours.

Know any official way to get rid of this? It's been a while, but contacting support over it feels like overkill.

For avatar, I think GOG caches PNG files slowly. Use JPG version of your avatar.