Full harness ON prior to engine start.
Shoulder / crotch strap OFF at 10,000 ft on climb, or at least after the After Takeoff checks, lap belt remains ON full time.
Full harness ON at 10,000 ft on descent through to engine shutdown.
Can't see the sense in keeping an inertial shoulder harness on en-route, I can't envisage any longitudinal decelerations en-route to warrant it. (Well, slamming into a mountain would provide one helluva deceleration, but you'll need a bit more than the shoulder harness).
FMC use - Don't fly the B737 but do fly one of the same family.
Takeoff : PF VNAV, PNF THRUST
En-Route : Typically PF PROGRESS, PNF LEGS, but commonsense applies to that selection which is most appropriate for the circumstances.
Descent / Approach : PF PROGRESS, PNF LEGS, the latter very important during VNAV approaches to monitor altitude constraints.