I get "Find out if Avallac'h's hiding something", two location markers on world map, one in Skellige and one in Novigrad, but when I oppen region map, I see no markers. Maybe there's a bug or something... I am unable to proceed further.

Does the skellige region map show a marker? Because that's where you need to go, if there isn't one try travelling to skellige maybe it appears as soon as you're in the region (was the case for me sometimes for other quests).
If it still doesn't show one ther are only 2 things you can do, eitehr you try traveling to the cave you need to go to and try if that helps or load asave before you started the quest.

"Find out if Avellac'h is hiding something" is a dummy. It is related to another quest with Ciri and Yennefer. Just keep following the other threads.

I found out that it was the "Child of the elder blood"(or something similar) quest that had to be done. Managed to proceed and on to another problem.