Blowing on or pouring water upon something already burning puts it out. The whole thing can be ignored if you don't have timed burning. Fragile objects can be smashed. The more complex version of this is to have breakable objects produce fragments, which can then themselves be handled and moved around. This requires dynamic object creation or something that looks like it.
Blades can cut through different materials.
Generally speaking, the real trick here, even more than dynamic object creation, is deciding what result cutting produces given the object being cut. Ideally one might want to allow the player to specify exactly how he wants to cut the object, but this gets into a syntactic quagmire. Back to Contents Division and Mixture. Divisible and miscible liquids. This requires, again, containers with known capacity.