Depends on the species of snake - the olive sea snake (Aipysurus laevis), which is the one most commonly encountered by diver, has the mouth you described. The stokes sea snake (Astrotia stokesii) has a larger gape and fangs, its often quoted that they can penetrate a wet suit - though the thickness of the wet suit is never discussed.
Most sea snake bites occur on trawlers, the poor animal has been hauled up onto the boat stressed and in a net with other critters. They often expend their venom on the fellow net travellers before they have the opportunity to have revenge on the real perpetrator.
Again species specific, a large number actually feed on fish eggs. Sea snakes that do feed on fish tend to go for small gobies, eels and other fish that can be trapped. I don't thing sea snakes will "do a python" and attempt to swallow large prey due to stream lining issues. Please correct me if I'm wrong.
The bite on the leg sounds real suss though.
