Now I'm sure if you go digging in the Red Forest like the Russians did at the start of the war you're going to have a bad time, but the exclusion zone has settled down significantly. Most of the highly radioactive isotopes have by definition a very short half-life.
Are you confident there are fewer microbes?
[1] http://www.chernobylgallery.com/chernobyl-disaster/radiation...
Extensively.
https://www.fda.gov/food/irradiation-food-packaging/overview....
At the low level, it boils down to the amount of energy an organism has at its disposal: prokaryotes have no mitochondria and thus cannot usually form multicellular organisms. If radiation hits an prokaryotic organism (i.e. a single cell) - it's alone by itself and probably well gone after the hit.
If radiation hits an eukaryotic (multicellular) organism, it still is able to compensate for that (to some degree) and still remains in the breeding pool for some time after the event.
The key difference between the two is the ability to reproduce itself after the damage.
So: thoroughly sterilised, if the FDA isn't totally off.