PoE spec is for ~48V. It's 48V, because "Telco power" is 48V. that's the voltage at which all the hardware at the telephone switching office runs at. That's the voltage that all Corporate Phone Systems run at. You can get some specialized rack mounted network gear that runs off 48V as well.
10BT only requires cat 3, 2 pair.
100BT requires 100MHz cat5, 2 pair.
gigabit requires 100MHz cat5e, 4 pair.
I cannot guarantee that the wiring will work correctly once you submerge it in water. I do not have a spool of cable and a bandwidth tester to see how the signal is degraded by wet cabling.
If you do buy "regular" network cable, be sure to buy a spool of the *PATCH* cable, not riser cable. riser is solid, whereas PATCH cables (or station cables) are stranded.
"Passive" POE puts power over the 2 pairs that does NOT have data on it. It is possible to run power on the data pairs, but I haven't tried doing so. It must be done in such a way that it won't interfere with the data signal.
48V is convenient, because of the telco industry: there are a LOT of 48V to misc voltage parts out there, especially in the surplus market. I have a bag full of 48-5V dc-dc converters I think I bought for $2 each.
The power limitation is partially heating, but most significantly voltage drop across the line. For every 100' of 26 AWG, expect 4 ohms of resistance in the cable. Double it because you need to go both there and back, and halve it because you use two wires for +V and two wires for -V. 48V @ 12W = 1/4A. 1/4A over 4 ohms is 1V drop. 1V / 48V = 2.1% power loss. Increase that to 1A for 48W, and you get 4V / 48V = 8.3% power loss and only 44V on the receiving end. Note that as you reduce your draw (say the batteries are fully charged and the rov is idle), the voltage WILL increase back to 48V. And as the cable length increases, your power loss increases too. Maximum distance on 100BT is 100m or ~300ft. so at 300ft, you get 12 ohms of resistance in the cable.