Hello Aliph! Yes, that's right. In Russian, the root is "нем"; "немой" means "mute" or "unable to speak". And as far as I know, the word "немец"/"немцы" didn't refer to the Germans only; initially, it meant something like "the Westerners" (probably those who were unable to speak Slavic languages). But the word "немцы" (plural) in Russian sounded pretty different then: the last syllable was stressed (now it's the first one). So, after a few centuries it had become a completely "independent" word and began to refer to the Germans only, who knows why. But I think I can safely say that the initial "mute" meaning has nothing to do with the current perception; almost nobody actually see the linkage between these words today.

Very interesting question!

Thank you Denis for the link to an excellent article of Wikipedia! So my souvenirs are correct. It comes from the protoslavic němьcь, pl. němьci, 'a foreigner' (from adjective němъ 'mute' and suffix -ьcь) I really appreciated your help! I love etymology.