Yeah, they drop things, but extremely rarely. Your best bet would be to put the Drop Cheat to x16 (you're going to have to deal with the low HP though), and get loads of Luck Panels. With all that you should have between 1 - 5% chance to get an item, depending on the difficulty.
no each difficulty has a 'class' of drops when it comes to stat chips
for instance the gold tricholoma on critical drops strength chips. you don't need a strength chip of each class, it just gets classified as strength + 2, etc as it means you get strength chips + 2 and above.