In terms of the written record, this cannot be authoritatively proven until the time of St. Shenouda the Archimandrite, who is remembered as the first Alexandrian theologian to deliberately write in Coptic (he, like St. Cyril, was given a classical Greek education and could converse and compose in Greek, but deliberately chose to write and preach in Coptic). St. Shenouda lived 347-465 or thereabouts, so his life overlaps considerably with St. Cyril (376-444), though he outlived St. Cyril by a bit, according to the tradition of the Church. There are other great saints of Alexandria who we know must’ve spoken Coptic by inference (e.g., St. Athanasius, who writes in his biography of St. Anthony the Father of the Monks that his teacher spoke no Greek, only Coptic, so St. Athanasius must’ve spoken it too), even though no contemporaneous written record exists of their preaching in the language.
Nope. The preexisting Alexandrian tradition was such that St. Cyril’s Greek formula (St. Cyril did not present his theology in Coptic) meant one thing, and the Alexandrians themselves by and large did not see that reflected in the Tome of Leo which was accepted at Chalcedon.
Except that it wasn’t a problem of how it was “translated into Coptic” – St. Cyril’s formula is in Greek originally, and the understanding of the same is rooted in the Hellenized Alexandrian tradition as promoted prior to Chalcedon (remember, St. Cyril died before Chalcedon ever happened; that’s why both sides can claim that they’re upholding St. Cyril’s uncontroversially Orthodox Christology – because he wasn’t around by that time to tell them which one actually was). It is not a problem of translation. It is a problem of different philosophical traditions informing the understanding of the same words in the same language. (And even it were a problem of Coptic specifically, what then of the Armenians, Ethiopians, and Syrians, none of whom spoke Coptic? What of the large number of Hellenized Palestinians who likewise rejected Chalcedon for some time after the Council? And for that matter, what of the “non-Chalcedonian” people who accepted it?)
But we do believe that there is but one nature in Christ. After the incarnation, it is no longer appropriate to say He is in two natures. That’s the whole reason why the OO fathers accepted “from two natures”, but not “in two natures”.