"The beach" is referring to the sand near the ocean , so saying "let's swim in the beach" doesn't work because that would imply that you are swimming in the sand, not the water.

Let's chill ON the beach. OR I am staying in a house BY (or BESIDE) the beach. Let's swim in the OCEAN. The ocean is the sea water that washes onto the beach. A beach is a relatively flat piece of land next to the water in an ocean, lake or river. It contains sand, rocks, shells and debris that washes up on the shore. If the edge of the ocean, lake or river are high cliffs or dense overgrowth then there is no beach. Since the beach is NEXT TO the water you cannot swim IN or ON the beach because it contains no water. You swim in the water, the ocean, the lake, the pool, the pond, the dam, the river, or the stream. You usually get into the water by walking on a beach to get to the water's edge. If there is no beach then you would have to jump off rocks or cliffs or out of a boat or swing on a rope tied to a tree that is growing on the banks of the water. A beach is generally covered in sand, shells, pebbles, small or medium sized rocks and sometimes hard mud (if the beach is next to a river or a lake or a dam.)

For your first question in American English, we use both. If someone wanted to go to the beach then they would say, "Let's chill on the beach" versus someone who wants to go to a location near the beach they would say, "Let's chill by the beach." Does that make sense? As for your second question both are correct the only difference is the location. Mostly because the beach isn't limited to being an ocean. Hopefully I answered your questions:)