How did clay and carbonates form in frozen comets? We don't know, but their presence may imply that the primordial solar system was thoroughly mixed together, allowing material formed near the Sun where water is liquid, and frozen material from out by Uranus and Neptune, to be included in the same body.

How do clays and carbonates form in frozen comets where there isn't liquid water? Nobody expected this.

Both of these are speculation. Hopefully in a few months I can tell you.

You can dredge material from near the infant Sun all the way out.