"My mind drifted, I steered by old habit and the boat stayed true to her course." This is a run-on sentence. The first comma should be a semi-colon (;), and a comma should be added after "habit" to make the remaining text a compound sentence.
"Suddenly, I felt an unnatural tingling at my back." To evoke suddenness and unnaturalness, cut this sentence to say: My back tingled.
"My mind was playing tricks on me, it had to be." This is another run-on. To correct it, simply change the comma to an em-dash (--).
"But this had never happened before, I was an old hand, had traveled maybe a hundred thousand miles at sea." This is yet another run-on. The first comma must be an em-dash or a semicolon. Refer to my examples above if you don't know what those are.
"I couldn’t concentrate on steering, and the sails all took to shivering(,) I was luffing up in the wind, and risked being backed into a jibe." This line should be two; otherwise, it's incorrect, and not in that stylish way that e. e. cummings' writing is. The comma I've put parentheses around should become a period. The comma after "wind" should be deleted.
"My breath came so fast now, and I had to slam a fist in my mouth, to not shout out for the captain to get up here, now, it was an emergency!"
"Suddenly, an explosion at the surface, as far as I could see! My puny lights were overwhelmed with brilliant light(word choice) all around me, at the level of the sea, and flashing yards into the air." To eradicate the redundancies and clumsiness of these lines, you should combine them.
"Tens of thousands of fish were leaping into the air, and each added its flash in the night, its moment of phosphorescent fame and glory. Together, they lit up the sea in a rare-to-human-eyes spectacle of light and sound." These lines use repetition improperly. "Flash" you used in the previous sentence; then, the fish "lit" the sea in a spectacle of "light."
"Each individual splash was like a raindrop that, added to its thousands of brother raindrops, created a soothing music, like that of rain." Not only do you reference rain twice in one sentence, you manage to confuse your subject and completely ruin your image. Try this: Each splash created a soothing music. This is a clear and strong image.
"All of a sudden, I heard a gigantic splash..." You overuse "suddenly" already--why try to hide it in this cliched phrase?
"I must have shouted out,..." Contrary to MTV belief, you don't have to add "out" to "shout" for it to be legitimate.
"Then I saw it(,) an immense form lifted itself from the water, graceful as a ballet dancer, its delicate lower jaw open to let a river flood out of its long mouth." That first comma should become a colon ( : ). Generally, the lower jaw is the one that opens. Regardless, the term "delicate" hardly fits with something as guttural as "jaw." Not only that, the sentence is passive, like many others; to improve it, I suggest reworking it this way: its delicate mouth widening to unleash a mighty rush of water.
"How that would have caused raucous joy in the old days of the grease pots and ivory." This is a fragment, but it misses its mark. Delete "how."
"I liked my life, too(,) no, I loved it(,) and did not want to sink to my death, glorious but unspoken, in the trough of the ocean." Make the first comma an em-dash ( -- ). Delete the second comma I put parentheses around. The part that was struck through is very purple.
"The giant sperm whale splashed about(+comma) happy as a baby in a tub."
"Then he suddenly became still, and his head turned slowly toward me; he lifted his head above the surface and worked his tail, maneuvering to slip in beside my boat." Let's rewrite this for a better impact: He stilled. His head turned toward me and lifted above the surface, his tail maneuvering to slip beside my boat.
"He turned his head and gazed at me with one big, meltingly soft eye." I thought his head had already turned toward your narrator..?
"yes, it wasn’t so very polite to show so much delight in killing and eating."
"His intelligence sought mine(,) it shone through that long gaze, and then he blinked and slid under. I sighed and closed my eyes. Yet the fear remained." Make that first comma semicolon. You recycled a form of "slide" from just a couple of sentences ago (He let himself slide downstream...). If you're going to emphasize that the fear remained, take out "yet" for a stronger effect.
"No, it was something else, and it was still prowling about, I felt it."
"As the minutes passed, though, I felt less and less anxious, and suddenly it was gone, like a bubble that burst with a pop, like the last scene of a cartoon. I was living a cartoon, inside the reel with Bugs and Tweety and Jules Verne." By referencing Jules Verne, you're asking the writer to see similarities between your writing and his. Needless to say, this is very pompous, and it ought to be deleted.
"The skipper came up the companionway then, and stuck his tousled head out the hatch." Delete that comma.
" The next morning, just as I was about to go down below for my tour in dreamland, dog-tired, listless, the captain asks me, as he’s gazing astern,..." Your sudden jump to the present tense should be permanent if you want it to work, but you go right back to the past tense in the next line. Just make this past-tense, too. I know you're going for a conversational feel, but it doesn't work like that.
The action in this flash is exciting enough, but the way you execute it requires a rewrite. A piece of so few words shouldn't have this much trouble. I invite you to dispose of my stylistic comments as you will, but each note about a comma requires correcting; I've left some sentences that require a comma alone, as they work well against the rule. Keep writing, champ!