Sidenote/nitpick: If you look at the historical record, while the Egyptian rulers did often marry in-family, there is fairly little evidence that these marriages were necessarily consummated. Most heirs came from concubines and the marriages were for the purpose of legitimization.
What was ancient Egypt?
The ancient Egyptians were actually not a single monolithic society with a clear beginning and ending point; at one point there was a clear division between a northern and southern kingdom, which were later united under one ruler. As they traded with and were invaded by other societies, intermarriage occurred.
Today’s Egypt is a great argument against the silly labels of race. As you travel from Lower Egypt to Upper Egypt (which I have done), the people generally get darker, but there is a real spectrum of people there. There are some people you would look at and say “white” and some “black” but mostly they are just themselves. I think this is probably the case through most northern African countries.
They were and are Egyptian, North African rather than sub-saharan classical ‘Negro’. Certainly not black for the most part.
Clines and clusters versus ‘race:’ A test in ancient Egypt and the case of a death on the Nile
Brace C.L.; Tracer D.P.; Yaroch L.A.; Robb J.; Brandt K.; Nelson A.R.
Museum of Anthropology, University Museums Building,Ann Arbor, MI 48109, USA
Abstract
The biological affinities of the ancient Egyptians were tested against their neighbors and selected prehistoric groups as well as against samples representing the major geographic population clusters of the world Two dozen craniofacial measurements were taken on each individual used. The raw measurements were converted into C scores and used to produce Euclidean distance dendrograms. The measurements were principally of adaptively trivial traits that display patterns of regional similarities based solely on genetic relationships. The Predynastic of Upper Egypt and the Late Dynastic of Lower Egypt are more closely related to each other than to any other population. **As a whole, they show ties with the European Neolithic, North Africa, modern Europe, and, more remotely, India, but not at all with sub-Saharan Africa, eastern Asia, Oceania, or the New World. ** Adjacent people in the Nile valley show similarities in trivial traits in an unbroken series from the delta in the north southward through Nubia and all the way to Somalia at the equator. At the same time, the gradient in skin color and body proportions suggests long-term adaptive response to selective forces appropriate to the latitude where they occur.An assessment of ‘race’ is as useless as it is impossible. Neither clines nor clusters alone suffice to deal with the biological nature of a widely distributed population. Both must be used. We conclude that the Egyptians have been in place since back in the Pleistocene and have been largely unaffected by either invasions or migrations. As others have noted, Egyptians are Egyptians, and they were so in the past as well.
They were and are Egyptian, North African rather than sub-saharan classical ‘Negro’. Certainly not black for the most part.
Clines and clusters versus ‘race:’ A test in ancient Egypt and the case of a death on the Nile
Brace C.L.; Tracer D.P.; Yaroch L.A.; Robb J.; Brandt K.; Nelson A.R.
American Journal of Physical Anthropology
Volume 92, Issue SUPPL. 17
1993
Pages 1-31
Abstract
The biological affinities of the ancient Egyptians were tested against their neighbors and selected prehistoric groups as well as against samples representing the major geographic population clusters of the world Two dozen craniofacial measurements were taken on each individual used. The raw measurements were converted into C scores and used to produce Euclidean distance dendrograms. The measurements were principally of adaptively trivial traits that display patterns of regional similarities based solely on genetic relationships. The Predynastic of Upper Egypt and the Late Dynastic of Lower Egypt are more closely related to each other than to any other population. **As a whole, they show ties with the European Neolithic, North Africa, modern Europe, and, more remotely, India, but not at all with sub-Saharan Africa, eastern Asia, Oceania, or the New World. ** Adjacent people in the Nile valley show similarities in trivial traits in an unbroken series from the delta in the north southward through Nubia and all the way to Somalia at the equator. At the same time, the gradient in skin color and body proportions suggests long-term adaptive response to selective forces appropriate to the latitude where they occur.An assessment of ‘race’ is as useless as it is impossible. Neither clines nor clusters alone suffice to deal with the biological nature of a widely distributed population. Both must be used. We conclude that the Egyptians have been in place since back in the Pleistocene and have been largely unaffected by either invasions or migrations. As others have noted, Egyptians are Egyptians, and they were so in the past as well.
Green. It is well-known among specialists in Egyptology but little publicized that the ancient Egyptians were green – does the idea of “Nile green” as a color ring a bell? 
Seriously, they were most likely “white” in the distinction between traits common to people of Western Eurasia, sub-Saharan Africa, and Eastern Asia/America that constitutes our basis for traditional race – but like most ancient peoples of the Near East they were fairly dark of skin tone by European/white American standards.
One key is in the depictions dating from the Amarna period, the one time during Pharaonic times when naturalistic art was followed. And the people are portrayed as I’ve described. For a good example, see the polychrome bust of Nefertiti.
Highly unlikely there was any at all IMHO. The Macedonians were notorious xenophobes ( Alexander and his officer Peucestes, later Satrap of Persia, being the exceptions that proved the rule ). In fact Cleopatra VII ( the famous one ) was the first member of her dynasty to learn Coptic - All the rest stuck to Greek. Further the dynasty rarely strayed from Alexandria, which was quite literally a Greek island in a Coptic sea. Indeed later members of the dynasty were quite often mired in constant revolts, egged on by the native Egyptian priestly caste, and barely exercised control anywhere outside of Alexandria. The Lagids ( Ptolemies ) were a particularly extractive, parasitic, and above all, alien dynasty ( relative to Egypt ).
True enough .
- Tamerlane
Tamerlane, I seriously doubt she would have learnt Coptic, as that language only developed with the rise of the Egyptian Christian Church. I’d suspect she learnt Middle Egyptian, although it’s possible she learnt Demotic. Edicts at that time were published in Greek (aristocratic), Middle Egyptian (quasi-aristocratic) and Demotic (the language the common people spoke, although I doubt many could read it).