That has to be the most confusing thing I've ever read.
Rainboe will correct me if necessary, but the answers to your sane questions are:
"When a captain is aboard a plane in flight, BUT has been asleep for hours, plans on being asleep for hours and is naked between the sheets in crew rest, who then is in command - that captain, or whatever pilot actually is awake, physically in cockpit and sitting in the left seat?"
Ultimately, the captain on his break. At the controls: the senior first officer.
"And does a pilot sitting in left seat while a captain is in crew rest have to be a captain as well?"
No.
Does a three pilot crew have to be 2 captains and 1 first officer?
No.