Answer: But my assurance was ill-founded, for, in spite of all my coaxing, Nab only circled around and around 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: "But my assurance was ill-founded, for, in spite of all my coaxing, Nab only circled around and around me until I was dizzy trying to keep track of him."
For is 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.
