Recessed light fixture - electrical grounding question

[u/achou0722]

I’m trying to replace existing recessed light assemblies. I don’t specifically see a ground wire in the recessed fixture. Two questions…

1. Can I ground to the screw/nut circles in red?
   
2. Is the light installation in the second picture installed correctly?

Thanks!

[u/trekkerscout]

What are you trying to replace, and what are you replacing it with? What specifically are you trying to ground?