It seems pretty obvious that gentiles shouldn't make Berachoth on any Mitzvoth (their 7 aren't exactly ritualistic, and they were not commanded in the rest of ours). But are there any Berachoth that they may/should say? Perhaps Nehenin (foods, scents) or Shevah (praises)? Maybe Shehehiyanu on certain occasions? Maybe even a judge who presides over a case (since they are commanded to have a justice system, which he is implementing)?
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We are instructed to answer Amen after a Bracha, if it's said by a Jew. If we hear the whole Bracha from a goy we also answer, otherwise we don't (we're afraid he said things we don't agree with) [SA & Rma OC 215:2]
So, apparently, a goy can say a Bracha, and we even say Amen. (Rma says
brochos with name of God - even Jews are not allowed beyond what was instituted.
as for thanking God without getting into saying God's name - absolutely. just like any one who benefits from someone else. my $0.02