The Stargazer PRC was published in Paths of the Righteous. It gets access to 2 hexes of choice and 2 oracle revelations (Coat of Many Stars and Star Chart) through the Mystery Magic class feature.
Questions
(assume a basic cleric for the base class)
1) Can a stargazer take the extra hex feat? (Similarly Accursed Hex, Ritual Hex, Split Hex)
2) Can a stargazer take the extra revelation feat?
Since the PRC doesn't actually get the Hex or Revelation class feature, strictly speaking, no. You can't take anything that requires those as a prereq.