If you click on an open barrel: It closes and may be dropped&dragged into your inventory safely.
if you've reached the tree: Open inventory, click on barrel to open it and throw.
The rest on the table is a waste of time. I spent 3 RL days in there to find a solution for the invisibility ring (was mentioned in the book) = NO way. Quest was taken out of the game.
Kiya, unforgiving ring-trauma