1. Still wouldn't matter. The area is far larger, and as the GM said, there are safe spots. Within 5 to 10 years the radiation is uniformly at safe levels (Exemption being those few old reactors that didn't SCRAM on their own).
-Earth land surface: 150,000,000 km2 Total nuclear arsenal: 17.000 warheads (current numbers) => 8000 square kilometers between individual impact sites. No significant build up of radioactive material is to be expected(Especially because a significant amount of the dust will blow into the sea). Sure, some cities will have been hit heavier than others, but well...
Besides, the damage is done. A nuclear warhead delivers 90% of it's energy in the first few weeks. Whatever anti radiation mesures we come up with are to late. Better start investing in anticancer therapies.
2. Nuclear reactors shut down automatically, unless they're caught in a blast zone(In that case they're vapourized). The amount of radiation released from those sources is neglible. Sure, some spent fuel basins might fail, but
3. The ozon layer defends against UV. Anti Radiation systems won't help you with that. Besides, the damage is already done. Little you can do but wait. Shouldn't take longer than 20 years.
4. Solar flares are something else entirely. Those are stopped by the geomagnetic field(won't be affected by nukes), and well won't be stopped by anti radiation systems either.
If you want something to fear, think of the earth's chemical industry. Massive silos all over the world, containing massive amounts of chemical products. The power grid has failed, so it won't be long before the temperatures in those tanks start to rise, and their contents are vented into the environment. Even that wouldn't be a critical event though. The areas surrounding those plants will have either been destroyed, or abandoned following the attacks.
Even more dangerous. The nuclear warheads kicked a tremendous amount of smoke and dust into the atmosphere. We're facing a nuclear winter, which temperatures dropping as low as Glacial levels.