Yes, homes built on a slab can still have radon. Whether the home is old, new, insulated or not and regardless of construction materials it can have radon. All homes, regardless of type of construction, should be tested for radon once per year per the EPA.
Yes, all homes need to be tested for radon. Radon can still enter the home through floor penetrations and the HVAC system and accumulate to elevated levels in the home..
All homes regardless of new or old, single or multi-story, slab or with a basement can have radon.
Yes, even if a home has a radon mitigation system in it, you need to test your home for radon as the EPA suggests. Regular testing will ensure that the radon mitigation system is working effectively.
No, testing can be done at any time of the year. Testing does require the home to have all of its windows and doors kept closed during the test, but central heating and air conditioning can operate. If the windows and doors cannot be kept closed during the test, it would be best to wait until the conditions allow for it.
The only known health risk associated with exposure to high levels of radon in indoor air is an increased lifetime risk of developing lung cancer. The risk from radon exposure is long term and depends on the level of radon, how long a person is exposed and their smoking habits. Smokers that are exposed to elevated levels of radon have risk of developing lung cancer increases.
The cost of reducing radon in your house depends on how your home was built and the extent of the radon problem.
Source: US EPA http://www.epa.gov/mold/moldresources.html