Most important factor in building muscle is total volume. Better to have more overall volume (total reps with time under tension) split over multiple sets than 1 or 2 sets to failure.
For chin ups, hold at top for 3 seconds and eccentric down for 3 seconds. Contract back as hard as possible.
Ring dips: Lock elbows at top and externally rotate rings to activate triceps. 1 sec hold at top, 3 second eccentric.
Rows: 1-2 sec hold at top, 3 second eccentric. Allow shoulder blades to relax at bottom. Keep gluts engaged, pushing hips forward.
Shoulder push up (pike push up on rings). Good regression of hand stand push up (harder than pike push up on floor). Externally rotate rings at top.
Rear delt fly. Smaller muscle groups (such as on the back of the shoulder) respond better to higher rep training.
