The most common document is a DD 214, which will list the veteran’s dates of service and campaign medals. You can also use other separation documents, such as documents showing service in Korea, Hostile Fire or Imminent Danger Pay on pay records, and also sometimes other documentation if you don’t have one of these.
No, your veteran is eligible the moment he/she earns the accepted campaign medals for overseas service.
The IRS determines the degrees of separation from the veteran that qualify for membership in a veterans’ service organization auxiliary. The relationship must be within two degrees of "consanguinity” in order to be eligible. That means two generations back (i.e. parents or grandparents) or forward (i.e. children or grandchildren).