Plumbers Goop is good for bonding plastics like that and is weather proof. Don't use superglue or 2 part epoxies, they just don't work.

Faux stone finishes don't stay on too well...I'd suggest a clear coat of Krylon or Rustoleum clear spray paint in a matte finish. Several coats provide a good sealer.

I feel your pain. I got a great angel and my son unloaded her onto our landscaping rocks. She fell forward and broke, and chipped in several places. We filled her witht he growing foam for the places we could not re-glue. The rest we used the GE-silicone II caulk like we use for BB's. WE know it will stick and with stand the elements.