Proto-Indo-European

It's interesting that that dative-"to be" construct for "to have" is also used in Finnish and Hungarian, and therefore most likely in Proto-Uralic as well.
Also, do you know if the presence of the PIE accent on a given symbol directly affects its reflexes? For example, if the first person plural pronoun was **wey rather than *wéy, would there be any difference in the derivatives?

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'."