How does nature dilute Ocean and Seas so that we can swim in them?
You hit on the main reason why sea water is fairly clean, which is the fact that the sea is so vast. Salt water kills some micro-organisms, but by no means all. The sea is teeming with countless trillions of them, some dangerous but most not. The sea is full of hungry animals which feed on animal detritus. Some of these animals are small, like anemones and corals, and some are large, mostly species of fish and hagfish. Some dead vertebrates like whales sink down into the abyssal ocean depths, where they provide a feast for various deep sea creatures. This has been going on for many millions of years, and many a dinosaur has been eaten and dissolved away by creatures beneath the waves. 

The many plants (sea grass and mangroves etc) and algae (seaweeds) also require nourishment, some of which comes from non-biological sources, and some from the excreta and decaying bodies of birds and other animals. Plastic is washed ashore and broken down into smaller and smaller fragments. Some beaches around the word are sufficiently polluted that they are classed as dangerous, and unfit to swim in, but may nevertheless seem to be clean. A few such beaches are in UK, so there must be some in America as well.