Some simple mental models: Think of the gravity connecting the moon and the earth as a string, and both bodies are rotated around its gravitational midpoint (which is afaik actually slightly inside the earth, but this still works), and you'll see that this will make the ocean bulge on both sides. But then we have the earth's own rotation to think about. The earth turns faster than the moon orbits the earth, and the bulges will drag behind, and the moon is affected by that, like the lure at the end of a string when you swing a fishing rod.

As for the Bernoulli explanation for lift.. try holding a sheet of paper in front of you, it's not solid so it'll bow down, with a nice wing-shaped form. Then blow gently over it, see what happens.