Give the stone slab to the old fisherman.
To explore the cave, you must find and fuse the light crystal in the alchemy shop with the empty lantern in a gold treasure chest at the beach.
You must battle and defeat monsters to find what you seek.
Thank you, and one final question is how do we get to the beach area?
I know the tavern guy tells us to go there I just don't know how to get there.
On the forest map, there should be an arrow pointing down.
Thank you again