To get the HM Surf you must go to the end of the Safari Zone. (It may take a few tries to do this) There will be a house. Inside the house will be a man. If you talk to him he will give you the HM Surf. Then once you defeat the Gym Leader you will be able to Surf on any large patch of water.
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Yes, Krabby is able to learn Surf. After all, it is a Water-type Pokemon.
On four Island you will need a Pokemon that knows Surf.
get surf at the safari zone (end of it actually)
I think the gym in fuschia city
You can only use Surf on calm water its not possible to surf on rough water.