SW corner - castle basement - clean out tiles, pick up tools and cannonballs, return to task giver
NW corner - kitchen - clean dishes, remove rats, find bag of flour, return to task giver
Upper NE - connect pipes, turn valve, return to task giver
Lower NE - tag 8 crew members so they go to the main room, return to task giver
SE corner - point all cannons in same direction, return to task giver
When you return to the task giver, you should get an experience reward. That is how you know that you completed that task successfully.
Get the key from Fabio in the main room.
The Beard Oil is in a gold flask on the table.