I just quickly looked into it with Dr. Google, and Medicare does cover the shingles vaccine as part of their preventive services, but is covered under part "D", the prescription drug plan, so you would need that, and pays for the doctor or other person for giving the vaccine, and co-pays apply. Part "A" or "B" doesn't pay for the shingles vaccine, so your doctor would have yo be able to bill under Part D or send you to a pharmacy accepting medicare Part D. If you go to one that is not, you may be responsible for the entire bill, maybe get reimbursed. I did not see a minimum age requirement, but the CDC recommends anyone over the age of 60 getting the vaccine, which is different than Medicare paying. I guess calling Medicare, your Part D provider, is the best thing.
If you already had shingles, the vaccine may lessen the severity.
Shingles is not contagious per say. If exposed by direct contact, when the blisters are open, they may get chicken pox, not shingles, as Kristen mentioned.