give evidence of puritan beliefs evident in the story thus far

I'm not sure what you mean by "thus far" but I can comment on the Puritan part of your question. Hawthorne places HSG in the 1850's and not the original Puritan time period of the 1630's. Hawthorne was hence not interested in the original Puritan themes of strict oppression and repression rather than the legacy left behind. We see the sense of intolerance of anything different and self-righteousness play out in HSG. THe whole idea about heavenly fate relating to wealth, through people like Judge Pyncheon, is explored in this book as well.