Quests in Grimoire are really just special Easter Eggs for which you get some experience points. You can see the list of all such finished quests in the journal.
Quest: Dream into the Sky Barge
Equip the Avian Helmet you find in the Eyrie and sleep in the tile with a circle in the North-East of the map. You will be teleported to a flying ship of a mage. After defeating the Watch Dog and the Mage, you can get some very good equipment.
Quest: Restore Crab into Shell House
You find a crab and his shell on the lake maps. Combine the two items and bring the crab to a shallow pool in the SE corner of the Waterport harbor.
Quest: Reach the Coast of Hyperborea
Go as far south as possible until you reach the ocean.
Quest: Catch a Rare Fish from the Well
There are three wells where you can catch three rare fishes. For that you need to first find four pieces of string and a hook in the Waterport maps and on the lake maps.
Quest: Unscrew Eye of Nerukzan
On top of the Nerukzan Pyramid, you need to put an item over the eye first to be able to touch it. Then a character with a good inspection skill needs to try several times to unscrew it.