My thoughts/response to the above:
1. a.) Does there necessarily have to be a kai/de format to the argument. We can see that kai is used to join multiple thoughts about the Son as in Hebrews 1:5 and 2:12-13.
b.) Even if God the Father is speaking in verse 13 does it have to be that verses 10-12 are a reference to the Father? It seems that, in the argument, the quoted verses are being used to talk about either the angels or the Son.
2. Hebrews 2:8 is actually referencing that mankind will have dominion over all things. Jesus, of course, is a man and he, too, has been given this dominion by God. Still, as we read down to 2:14, there seems to be the implication that Jesus was made like mankind (as in Philippians 2) so that he could be the sacrifice for all who will have dominion. “Partook” of the same seems to imply that he took on something that he wasn’t originally.
3 b.) I looked up both of the verbs and they both appear to be third person singular which can be translated he or it. And they both appear to mean, “says,” although one could be more like “declares” or another English synonym. Even if one verb is more likely used of God speaking and the other to indicate what Scripture says, are we not told that men spoke by the Holy Spirit in Scripture? And, therefore, what is being quoted in Hebrews is divinely ordained anyways? Even if God is not noted to originally be the speaker in the Psalms, NT theology is telling us is that He is. Even Jesus, when he quotes David speaking in Psalm 110, says, “Then how does David, in the Spirit, call him ‘Lord’?” (Matthew 22:43)