For (p): In zero gravity, SHM may or may not be possible, it depends upon system. For example, a simple pendulum will not perform SHM, but a springblock system can perform SHM in zero gravity.
For (q): If no restoring force, then SHM is definitely not possible.
For (r): Mechanical energy may be conserved in motions other than SHM.
For (s): y=sin2ωt represents an SHM.