Don't know anything about the Newsoms, but would like to know if you can locate this family on the 1860 census. I can answer you question about discharge, the expression meaning he has been released from military service. Since he had been very sick earlier, we can assume that this was due to prolonged illness. Specifics should be in his military record.

It's very difficult to 'prove' that a specific soldier is who you believe him to be. In nearly every case, identification is based on name, residence and sometimes age. If no one else with the same name as your ancestor lived in the county or parish in which a company was recruited, we can safely assume a positive connection. Sometimes pension application include useful information as well.