Your second question asks if this same flight crewmember may
participate in the activities previously listed during a rest period if
the work was done for another company, not ABC,and whether the flight
crewmember could then accept an assignment with ABC for flight
operations under Part 135, at the end of the rest period.
The answer is a qualified yes. ABC, as the certificate holder, has no
way of forcing the flight crewmember to rest during a rest period.
The prohibition against "other commercial flying" during a rest period
applies to flying assigned by the certificate holder. The other
commercial flying done by the flight crewmember does count against
the daily 8 hour limitation if it is done before the Part 135 flying,
and also counts against the pilot's quarterly and yearly flight time
limitations. For example, 2 hours of "freelance" flight instruction
by the pilot during his rest period limits him to only 6 hours of Part
135 flying time during that 24 consecutive hour period. Any other
commercial flying done after the Part 135 flying does not count
against the daily limitation, but still counts against quarterly and
yearly totals.
An additional caution is that it is a violation of FAR 91.13 for a
certificate holder or a flight crewmember to operate an aircraft in a
careless or reckless manner so as to endanger the life or property of
another. Lack of rest of the pilot is certainly a circumstance which
could endanger others, and it is not necessary that the situation
devolve into actual endangerment for there to be a violation of FAR
91.13. A certificate holder who uses a crewmember with knowledge of
his or her lack of rest may be equally culpable along with the flight
crewmember.