Do Cargo flights carry anyone other than the crew?
Yes, cargo aircraft are like other aircraft in that there is generally at least a jump seat available. Especially larger aircraft will also have additional jump seats, a lavatory, and a galley. This area can be used for relief crew, or other crew that are just deadheading.

There are exceptions though. The upper deck of the 747 is larger than just the cockpit, even on the cargo versions. There is more room in the back for additional crew. The An-124 and An-225 also have additional space for crew behind the cockpit. The extra crew can be loadmasters, navigators, mechanics, or other functions that can make it easier to operate in and out of airports with less services available.

Here is the upper deck of a 747-400F: