Very cool character!
From 2.8x but the concepts are still relevant.
Basically the holster-strap should be rigged the same way as the shirt, and the holster-pocket should get its own bone.
To help with strap-weights this vid is useful:
Search for “rigging clothes/equipment in blender” for many other examples (some are over an hour and quite detailed if needed)
…for the eyebrows - I would maybe treat them as a separate object and weight them by the eyebrow bones. 
Good luck.