This test is probably not being used for "what kind of cancer" but as a cheap and easy way for yearly/bi-yearly tests of the general population as part of prevention.
With a 1% false positive rate that won't work I guess. False positive rate needs to be much smaller.
I don't think they do. If someone tests positive, I imagine the next step would be to do more thorough (and expensive, and time-consuming) tests and find out for sure.