"When the men enlisted, did they take their pictures?"

Not Usually, The Pictures that were taken were for the profit of the photographer. The soldiers who could pay for them, would send them home to family.

"What kind of identification did they carry in case they were killed."

Individual soldiers would write their names on a piece of paper and pin it inside their jackets, some would possible carry a wooden or metal (Brass) disk with their names carved, or scratched, into them, maybe their regiment. Most identifing of the dead was done by friends or other family members in the company.