3. How did they get the Enterprise under water without the natives seeing them? It's not like they were far out in the middle of the ocean, even with all the lights out (?!) the ship would be visible descending at night.
We have no idea how bright or dark the nights are on this planet, or even if the natives can see well in the dark. Ever go out into wilderness on a moonless night? Amazingly dark except for the starlight. Also, the ship could have descended into the ocean 30 miles away approached land underwater. At 30 miles distance even the huge E wouldn't appear very big. I often see huge container ships leaving San Francisco Bay from my bedroom window, and when they're about 14 miles miles from me (halfway to the Farallon Islands) they look pretty puny.