One could describe the 13 ikkarim as a psak for mandatory beliefs.
I agree.
One should note that they were not universally accepted, even today. See… the Machnise Rachamim prayer in the Selichot service
That is an egregious error, which I’ve pointed out in the past (with sources). I don’t have time now, but after Shabbos I’ll bl”n post a link to a teshuvah in the Igros Moshe on it (which I don’t think I’ve posted yet).