Proto-Indo-European

That depends on the language. Aside from languages that preserve the accent placement itself, there are also languages that preserve indirect traces of the accent. Verner's Law in Germanic is a good example of that.

Ok. Do you have any idea how PIE *méme ~ moy reflexed into PG *mīnaz?

I don't think they did. *mīnaz probably goes back to an earlier *meynos, but I don't know where that came from.

It could be related to the *-nos in *(h)óy(h)nos, and then the *mey- would be an e-grade of the PIE *moy. But I don't know how the *-nos suffix works, and it seems to be in free variation with *-kos and *-wos. Is it a known suffix?

As far as I know *-nos forms adjectives from verbal roots, but I'm not aware of any other use.

Could *éy- have been a verbal root besides a pronoun?

Why do you think that?

Since in the etymology for *óynos it says, "Perhaps built on the pronominal stem *h₁ey- 'he, she, it'."