If hemochromatosis is a genetic disease, should other family members be tested? Which ones and when?

Yes. Hemochromatosis is the most common of genetic diseases. It can have variable penitrance and manifest briskly or insiduoulsy. It is usually not manifest until the 4th or 5th decade of life and usually in males since women lose blood/iron with menses. A blood test can be done to diagnose and for genetics. Counsel with your pcp, hematologist or geneticist. Great sources on the web. I have it!
Siblings and childre. Hemochromatosis is inherited as an autosomal recessive manner. That means for any affected individual (person with hfe). The risk to any brothers or sisters of an affected person is between 25-50% depending on the carrier status of the parents. For children of an affected parent, the risk is about 5% based on the carrier frequency in the general population but could be up to 25%.