"Do you speak German?"
Translation:Вы говорите по-немецки?
This is a really complex question. We do drop pronouns sometimes, but usually when we have a context. Duolingo sentences don't have a context, so dropping pronouns sounds very wrong.
Pronouns are often dropped in colloquial speech, and less often in formal speech. Also, pronouns are used when the context doesn't change.
По-немецки (can be any language) literally means "in a German way". That's an adverb and it answers the question "how?". Как? - По-немецки. "По-" is an indicator here that it's an adverb. Adverbs end with one "и".
Немецкий is an adjective. It describes a noun, though this noun can be omitted. Немецкий язык. Он говорит на немецком языке. Он говорит на немецком. It ends with "ий" (in nominative case).
«По неме́цкому» means something different (e.g. «оце́нка по неме́цкому» is the 'mark in the German class', «уче́бник по неме́цкому» 'a German textbook').
Theoretically you could use «по-герма́нски» if you mean the Proto-Germanic or Common Germanic, the common language that is the ancestor of all Germanic languages nowadays, but I doubt you’d find any speakers. :D
Also, theoretically, you could ask this if you’re looking for a speaker of any Germanic language (from Faroese to Afrikaans, doesn't matter which one), but this is likely to be expressed with «Вы говори́те на (како́м-нибудь) герма́нском языке́?».
I'm not sure about 'more correct' (I think it sounds somewhat less natural, because we more often omit the noun than use it), but I think it should be accepted as an alternative.
All adverbs that begin with по- and en in -ски are written with a hyphen. I have no idea why. Russian orthography is not really logical when it comes to adverbs and adverb-like phrases.
The version with the pronoun is the 'default' one, it's a neutral version you can use anywhere. It's better to learn this version.
Version without pronoun can be used in some contexts. Often, pronoun-dropping shows the text is about the same person, the topic has not changed. But Duolingo can't show context, so it can't teach you when it's appropriate to drop pronouns.
The issue is pretty complex, in colloquial speech we drop more pronouns than in written texts, but in general I think it's better to learn the variant with the pronoun.
I am just a Russian student, but I have noted that people insist in treating Russian as Spanish or Italian, just because Russian has verb conjugations. People should understand that Russian has its own rules. Dropping the subject is used just in some specific situations and just with some specific verbs, like думать (to think, to suppose). In most cases, pronouns won't be dropped in Russian like it is in Romance Languages.