Sorry I cannot address the questions about measuring body fat etc. because I don't know anything about this. The bone scans are pricey, but the first scan I ever got was a free screening done at a local pharmacy. It is not unusual for free screenings to be done at chain-type stores or even local health clinics or heath "fairs". The typical screening is done on a little device that measures bone density in the heel of your foot. They typically give you a report right there on the spot that tells you where you are on a "scale". It will recommend you see your doctor if the test shows you are in the abnormal range. It's not as good a test as the expensive scans, but it can help you decide if you need to seek medical advice. Plus, you can take the free screening report with you to the doctor to show why you are concerned. It came in handy for me. It's one of the best free things I have ever received!
Best wishes to you, bablymers mom