Do bullet cases serve any purpose?

Drop one on the ground and pick it up. It will give you the ammo.

Wait. Do you mean crates of ammo or casings? If casings, they're used for crafting ammo.

Unbugged, they can be used at reloading benches (along with other ingredients) to make new ammo.

Okay. Thanks. Do they take up weight though?

The cases I haven't looked into enough to fully understand their value, and "breakdown ammo", at the ammo table, does breakdown refer to taking a bullet and melting it into something else, or does it mean taking something else and "making" that "breakdown .9mm" ammo for example? I haven't tried it yet, but don't want to lose valuable ammo just yet. Too busy doing everything else in the game.

What about NCR Dollars? Are they only good for selling for caps or do they have another purpose? Is that what you need to buy stuff at NCR places?

Yeah "breaking down" the ammo refers to disassembling it into it's component parts. (To, for example, get the shell primers from ammo you don't use, so you can then use them to make the ammo you do use.)