Are there, on the ocean floor, areas where there exists a
concentration of rocket parts associated with each launch site?
Trivially, yes; for example, most launches from Florida have been to the east, you can imagine a triangle-shaped area extending out from Cape Canaveral into the ocean, defined by the allowable launch azimuths.
Most of the boosters would land in this area.
What happens to rocket stages that land in the oceans...?
Most first stages aren't (relatively speaking) going that fast, so they don't burn up, but suffer mechanical damage when they crash into the ocean. Here's a picture of remnants from a Saturn V first stage after many years in the ocean.
Source 1, Source 2