Does the Coptic Orthodox Church believe and teach Adoptionism? What about the Ethiopian Orthodox Church?

I have never encountered this claim. Traditionally, it is Nestorianism - the historic opponent of Coptic Orthodoxy - that has borne the accusation of adoptionism.
Does the Coptic Orthodox Church believe the Bishop of Rome to be a “first among equals” like the Eastern Orthodox?
There is no definite answer to this one. Why? Because the Protocol for dialogue between the CC and COC which was determined in 1986 (and which guides that dialogue to this day), and containing all the relevant concerns between the CC and COC, does not include the papacy or ecclesiology. Basically, this issue has never come up.
Of course, the papal dogmas from V1 poses a natural field of disagreement and dialogue. But as far as recognizing the bishop of Rome as
primus inter pares, what would govern the matter from the COC’s perspective is the following agreed statement from the Joint Commission:
“
The process by which it (the union) is achieved is that two Apostolic Churches, equally and with mutual respect, come into full communion again on the basis of faith, the traditions and the ecclesiastical life of the undivided Church of the first four and a half centuries.”
On that basis, I am confident that if and when reunion is achieved, the COC would agree not only that the bishop of Rome is
primus inter pares, but also that this title is not a mere honorific, but rather entails a real authority.
Blessings,
Marduk