Radiation existed long before Man, even though the no-nukes would have you believe otherwise. The US Geological Survey has a Radon WWW Page. It contains a great deal of useful information, maps of radon levels in the US, and links to other sites. Note that even though most of the heavy elements are alpha emitters, they can still be dangerous, if they get inside your body. Your skin stops alpha particles if the source is outside your body, but your internal organs and tissues have no such protection.
Radioactive dust can be hazardous.
It's true, it contains radioactive decay products from naturally occuring Uranium and Thorium. As an experiment, I wiped some dust from the TV screen onto a tissue, and placed it in front of the radiation detector. The Radon is produced by Uranium that naturally occurs in the soil, after a rather long decay process. Radon has a half life of just under 4 days. The Radon decays into Polonium, which them decays into Radium B, an isotope of Lead.