You can left click vases to open them, without smashing them, and broken vases don't contain anything. There are some indestructible weapons, and ranged magical attacks can also damage most doors and containers.

You can equip a fishing rod to use as a weapon, but there is no way to use them to fish.

With traps try to find a way around or trigger it from a distance before using a trap disarm kit, and for chests search for a key before using a lockpick. Lockpicks can be crafted, as well, but often there is a key, switch/lever, or other means to open locked doors and chests.