Almost. If nuclear war starts there will be regions that will be not nuked (neutral countries, territories not threatening either side and so on). Basically most of northern hemisphere would be destroyed. After the war clouds of extremely radioactive dust would kill most of the life, mutate rest (making for example most mammals unable to get pregnant). Southern hemisphere would be mostly untouched but the radioactive clouds and winds would take it tool for hundreds of years. Majority of life would die out (human race would most likely survive despite scary stories - it would just go back to what it was 100 years ago). Casualties would be counted in billions. Most flora and fauna would be destroyed. Dusts in atmosphere would make changes to the planet cooling it a bit. It would take hundreds of years for our civilization to get back to what it is now (but most northern part of globe would stay uninhabitable). The hope to restore humanity would be in hands of Australia, New Zealand, Argentina.
In this scenario, how long would it take for the radioactivity to completely disappear and start re-inhabiting and re-populating the northern hemisphere?
It depends largely on the type of blast, an air blast, which is the most destructive to property and buildings is the least contaminating in it's effects; e.g. Hiroshima and Nagasaki.
However, if you let the bomb detonate very close the surface, you get less destruction in terms of the blast, but you get insanely high radiation levels for a long time afterwards. Analogous to Chernobyl.
Its not that easy. Radioactive materials dont just disappear. It would take probably around ~100-200 years for humans to evolve to be partly immune to radioactivity (the same way we "evolved" to be partly immune to coal vapors and other toxic waste in our air) and reduce amount of sick/sterile people. Then humans would need to slowly remove or neutralize radioactive content - 200 years sounds right for humanity to find a way of doing this (as of now there is no mass way doing so - but I believe humanity would come out with solution if this would be the way for civilization to survive). The process probably would take ages - started with regions less contaminated (Islands etc) and moving onwards avoiding direct impact zones.
You're not thinking very hard. How long does it generally take to get a new breed of dog? How many generations of E. Coli will occur over 200 years? Assuming a human generation length of 25 years, why would there be no evolutionary change over 8 generations?
To within measurement error, all attributes are pre-existing attributes. It's called "natural variation" and is the universally-accepted explanation for why we have sexual reproduction instead of budding. Right now, some people are more radiation-resistant than others.
