How can people walk around without getting cancer?
The three factors for protecting oneself from radiation and fallout
are distance, shielding and time.
- Distance - the more distance between you and the fallout particles, the better. An underground area such as a home or office building
basement offers more protection than the first floor of a building. A
floor near the middle of a high-rise may be better, depending on what
is nearby at that level on which significant fallout particles would
collect. Flat roofs collect fallout particles so the top floor is not
a good choice, nor is a floor adjacent to a neighboring flat roof.
- Shielding - the heavier and denser the materials—thick walls, concrete, bricks, books and earth—between you and the fallout
particles, the better.
- Time - fallout radiation loses its intensity fairly rapidly. In time, you will be able to leave the fallout shelter. Radioactive
fallout poses the greatest threat to people during the first two
weeks, by which time it has declined to about 1 percent of its initial
How can people survive the attack?
Even in apocalyptic situations, it's difficult to get 100% mortality rate. So of course there will be survivors not killed by the blast or radiation.
Assuming the human mortality rate for Judgment Day after a decade was 99.9%, that still leaves 7.046 million survivors. Even if the mortality rate was 99.99%, that's still close to a million survivors.
How are the survivors walking around under open sky?
(Note: I believe in the first 2 Terminator films, the scenes set in the future show dark skies, which could well be due to smoke/ash in the atmosphere.)
Current models of the nuclear winter resulting from launching the world's entire nuclear arsenal (most versions of Judgment Day only involve launching the U.S. and Russian nuclear stockpiles) predict average global temperatures dropping by 7~8 °C (way more than that during the ice age, which was -5 °C) for a decade, then dissipating to -4 °C, though certain regions over land could see drops in temperature by as much as 20 °C, and places like Iowa would see subzero temperatures for over a year.
But this doesn't mean people can't walk around outside. In fact, food production could resume within a few years, though extreme drought and high UV radiation would reduce yields to levels not seen since the Dark Ages.
Terminator: Salvation is set 22 years after the Judgment Day in that timeline (July 25, 2004), so it's pretty reasonable to expect the small number of people who survived the initial attack and famine to be able to walk around outside without any protective gear or heavy clothing.
In Terminator 2, Judgment Day was August 29, 1997, and the T-800 & T-1000 are from 2029, a full 32 years after the nuclear strike. So, the environmental effects of the strike would be even less significant at that point.