It is a fish indeed. To be frank, they learn few attacks at first. Leviathan knew the Dragon-type Dragon Breath at birth, but according to the Pokédex that is unusual. However, as their father is a high-levelled Gyarados, they might have inherited attacks from him.

At first, training one will be much like training a Magikarp; you'll have to use another Pokémon to do the damage. However, unlike Magikarp, Feebas can learn attacks from Technical and Hidden Machines. I know for a fact that they are compatible with Ice Beam; I also suspect Surf would work. That last one can be obtained by defeating Morty, if you wish.

[He finally breathes.]

Do you have any other questions?