You are not talking 10 or 20 years. Hundreds or thousands of years is closer to the impact.
There was enough nuclear weapons stockpiled by the US and Soviet Union alone to wipe out life on the planet a hundred times over. The video game is a representation fantasy and is fun to play but doesn't really reflect the effects.
I assume by Fallout you are referring to the video game series.
The premise of Fallout was based on the very real possibility of there being an all-out nuclear war during the cold war. People really were building bomb shelters in their backyards and smaller versions of the Vaults from the game were actually built. One such structure exists just outside of Washington DC, deep under a large luxury hotel. It was designed to house the President, Congress, Senate, plus a few hundred more staff. It was believed that in the event of a nuclear war, the government would continue from that bunker. Another such bunker was built deep in the Colorado Rockies where the US headquarters of NATO is located.
A lot of TV and movies during the 1950s and 1960s included mentions of nuclear war, underground bomb shelters or vaults where people would take refuge until the radiation from the war had died down to the point where it was safe to come out.
Of course, the reality of such a structure like the vault is pretty ludicrous since it would have to remain operational for hundreds, if not thousands, of years while the radiation from the bombs dropped to marginally safe levels.
Had a true global nuclear war broken out between the US and USSR, the world would have been rendered practically barren and lifeless for 10s of thousands of years. There would be no more human race. Maybe if we were lucky, aliens would come across a few ruins of our civilization, and from the elevated radiation levels, figure out what had happened.
It depends on the scale of the attacks. If it is worldwide then yes its possible. The radiation would linger for thousands of years.
FYI: The OP didn't specify, but Fallout is a post apocalyptic video game set in an alternate universe.
Depends. There is 'dirty' bombs that are designed just to spread radiation, to kill people but not destroy infrastructure. Then there are many different sources of radiation - Some elements have a half-life of 1,000 years & some only -5- years.
I don't think so. I think the world would recover in a matter of years and government would be quickly restored to nations all across the world. The country might be a bit more desert due to detonations. But I'm sure it won't be large scale and it would be a matter of 10 to 20 years for a recovery. What do you think?