Anybody that's faced the issue I'm trying to solve will probably recognise it from the subject line.
The Ф key must be pressed twice to result in an Ф. One press = a, two presses within a second = ф. Holding it down results in the subject line.
I'm using the native Ukrainian keyboard on Win10. Also Colemak and UK keyboard layouts under UK English.
That sounds very strange to me. I'm using a few keyboard layouts myself (also Windows 10), one of them is Ukrainian Enhanced Keyboard, I have never experienced an issue like the one you've just described.
Also, does the problem occur only when you're using duolingo or it's a more general Windows problem? If you open a notepad, switch to the Ukrainian keyboard and type ф do you see the same result?
Is it true for other keys as well? If you long press say q using the Ukrainian layout, will you see qйqйqйqйqйqйqйqйqйqйqйqй?
Also, the "a" in your subject line is English (not Cyrillic), the "ф" is Cyrillic, I don't know whether it's important or not, for now just an observation.