There is no key for the spider room. Put out the torch beside the locked door to open it.
You need coal (Fergus' room), salt (citadel kitchen) and sulphur (gay medic's room) to make the explosives. With all 3 items in the hero's inventory, mix the coal and salt, then drag the sulphur over this mixture. In the smith's room in the citadel, you need to drag and drop the newly created explosives onto the forge (there is only 1 spot in the room that is active, so it is not hard to find).