long answer: see https://forum.duolingo.com/comment/2591660/Formatting-Codes
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Nice example:) Although with the adjective good it does sound better, instead of "He speaks good English", to say "He speaks English well". That's probably beacause when describing a verb (“speaks"), we usually use an adverb ("well"), not an adjective. But I guess you could look at it as if we were describing the noun "English", and not the way he speaks English. Good, well, bad, badly, I don't know, it's a bit of a mess...
No, it's just the first. You could say "jag talar svenska dåligt", but it's much more idiomatic to say "jag talar dålig svenska", so the first would demonstrate just how badly you actually speak Swedish. (I actually did this the last time I was in Sweden, just two months into the Swedish course.)
I think what your going for in the english translation is "he speaks poor Swedish" this shows me that the tables have turned and du talar dålig engelska ;). Your english translation leads me to believe that the subject is verbally conveying ideas that do harm, in Swedish. Not that the subject is speaking Swedish with poor pronunciation or grammar.
There seems confusion here between adjectives and adverbs in the English translation. "Bad" is an adjective so you cannot speak bad. I also doubt there is a language called "bad Swedish". The best translation is "He speaks Swedish badly", where the adverb describes the way that the Swedish language is spoken. This form is accepted as correct by the system, but the "other correct solution" is itself bad.