Answer:
But my assurance was ill-founded, for in spite of all my coaxing, Nab only circled round and round me until I was dizzy trying to keep track of him.
(Note: There could be some definite improvements for all of these sentences. What I'm about to say may not be consistent with how other people learned.)
Explanation:
"At the sound of my voice there was a sharp little bark from behind, such as Nab alone could give when I had an exceptionally delicate morsel for him."
The sentence, "At the sound of my voice there was a sharp little bark from behind" is an independent clause; there should be no comma after an independent clause.
"But my assurance was ill-founded, for in spite of all my coaxing, Nab only circled round and round me until I was dizzy trying to keep track of him."
For is a conjunction; any conjunctions after an independent clause are fine.
"Nab suddenly made a dash so close that his flippers brushed my side. He snapped the fish out of my hand, and in the same instant he was again beyond reach."
There needs to be a comma after "instant" so that it would make an independent clause after it.
"By this time I had begun to feel pretty well exhausted, and when I suddenly thought of the undertow, I decided to swim back."
A comma should be placed after "time" to make an independent clause after.
