The object of a sniper is to get close.
Actually, quite the opposite. The sniper uses the extended range capability of his weapon to his advantage every time he has the option. The object of the sniper is to get close enough to ensure a hit, and not an inch closer.
Snipers are poorly equipped to handle anything up close and personal.
"Close" is a relative term. The closer you get, the better your chances of hitting are. It's the same with hunting; why take a 600 yards shot when you can take a 400 yard shot with a little woodcraft.
They do, in fact, operate in teams, and are as well equipped to handle VERY close combat as any other two-man team.
