The vacuum in space would kill you first in space because the vacuum would collapse your lungs instantly and then death would follow later because you can get no oxygen in space.
Space contains no oxygen so when you get into space without a space suit the lack of oxygen would easily kill you first in space.
We need oxygen to breathe and without the oxygen you would suffer brain damage and then die within about 20 minutes or so.
However you would likely die due to the vacuum in space that would collapse your lungs instantly and prevent you from breathing anyway.
There are no amount of dead bodies in space.
There have been 3 astronauts that have died while in space but the astronauts bodies were recovered and brought back to earth.
So that means there's no dead bodies or dead astronauts in space.
Also if the astronauts bodies were left in space floating around then eventually the dead body would decay much faster and basically disintegrate and degrade really fast as within a year or two.
When someone dies in space their body would be floating around in low Earth orbit (e.g. at the altitude of Hubble or of the ISS or of Tiangong), the small amount of atmospheric drag that exists at that altitude would cause the corpse's orbit to degrade with a timescale of a few years. It would then burn up and disintegrate in the Earth's atmosphere.
So the body of the astronaut would not just stay there for years and years and eventually there would be no dead body up there.
There could have been an astronaut that died years ago up in space and their body could've remained up there but the astronauts body would degrade and go away soon.