Are isotope bone scans safe?

Very safe. Injection of isotope technetium 99m mdp and visualization of skeleton looking for areas of abnormal uptake. Side effects include sometimes some bleeding from injection site. Isotope usually does not cause any allergic reaction. Lie down on table with cameras taking images of skeleton. Relax.
Yes... Yes... there is a small amount of radiation exposure from the radiotracer which has a half life of about 6 hours and is excreted in your urine and should be mostly out of your system in approximately 24 hours after injection.