Hi,
1. When a relay is labeled something like "5V, 12A" what is what?
Coil is for 5V and the relay contacts can handle up to 12A (non inductive current typically).
2. How much current do these draw, just as a guess?
Somewhere between 50mA and 150mA would be a guess. Probably in the upper half of that range, given the contact rating.
Is it at all possible I could directly wire this to an Arduino microcontroller?
Not really, besides the drive current, you also have to consider spikes from the relay, as they might not be properly dampened by the conventional diode protection.
3. Anything else I should know about relays?
You should allways mount a diode (or two, depending on the configuration) to protect against inductive spikes.
It should be the fastest diodes that you have, which is able to handle the spike energy.
And of course, a simple transistor driver, to go in between the controller and the relay.
My knowledge of electronics is limited, so any comments you have are welcome!
With that comment, I'd advise against trying to complete an underwater robot - better start with something simpler.