Yes. Yes they can. Such records as previous criminal convictions, or dishonorable indebtedness can prevent enlistment.
One can become a private military contractor by joining the Military service. They earn from $500 to $750.
Joining the military in the US is voluntary. He doesn't have to join if he doesn't want to.
Rick Santorum did not serve in the military, though he has expressed support for military service and veterans throughout his political career. His children have not served in the military either. Santorum's family has been involved in various public service roles, but there are no records of military service among them.
The United States Military does not prohibit online gambling. Online Casinos have nothing in there terms of service that would disallow a member of the military to gamble online. So to answer your question, being a member of the military does not restrict one from gambling online.
Go to the US Archives. If you go to the .gov website for the US Archives, you will find a link to military records. You can fill out a form online, and if it is available they will send you the records for a small fee for copying charges.
You can get free copies through this site http://www.archives.gov/veterans/military-service-records/get-service-records.html
Of course! They want to make sure that you are healthy and fit enough to undergo service.
If all else is good (records, health, age, etc.) it's done all the time. Even leaving one service and joining another one is common (being honorably discharged from the Navy and joining the Air Force for example); and it all counts for the "20" (twenty years service retirement).
Try here: http://www.archives.gov/veterans/military-service-records/replacement-medals.html
Start by checking any military records or documents your family might have. You can also reach out to the National Archives or the appropriate branch of the military for service records. Additionally, consider asking other family members or researching unit histories to see if you can identify which unit your grandfather served in.
I'm going to assume that you were in the military. Most background checks do not delve into your military service records, only what kind of discharge you had. For a civilian records check you should be okay.
Typically, military clergy (Chaplains) have completed their training prior to joining the military and serve as officers. In some cases, the US Military may pay tuition for a clergyman to complete his education prior to entering active duty service.