Personal opinion on the Peter/church thing, I'd suggest that Matthew is a gospel written for a Greek speaking Jewish community. It seems like an appeal to a more Jewish form of Christianity, and, if it was written late in the first century, then one has the obvious resistance in some branches of Christianity towards moving away from that. So an appeal to Peter as the authority on church matters may have been more in line with a unifying (on this issue) branch of christianity which still retained essential elements of Judaism. eg. see The Diadache of a little later for how Christian beliefs were superimposed on Jewish rites in a way to allow for Gentiles.
On the Mithras ideas, I'll defer to Clauss (The Roman Cult of Mithras). So much isn't known and so much of what was once 'known' seems to merely be clumsy nineteenth and early twentieth century supposition based on not a lot. I do know that Praetextatus was clearly not a christian - Jerome makes that point inescapably obvious in letter XXIII by contrasting his hopes for an afterlife with those of a good christian woman who'd died.