Does the location of the PokéStop you get an egg from influence the Pokémon in it?

I read that you get more fish Pokémon near beaches, etc. If I get an egg from a PokéStop in a beach area, will it be more likely to contain a fish Pokémon, or will the contents be random?

Eggs are randomly generated. Meaning, there is no correlation between the location where the egg was collected and the Pokemon inside.

Similarly, there is no correlation between the hatch location and the type of the Pokemon collected.

Eggs have been confirmed to be set as a Pokemon type at the time of egg collection. See this resources dump.

I don't think so. I've never once seen any water type in the wild (live in the mountains) and yet I've gotten multiple water types from eggs.