"I speak English well."
Translation:Я хорошо говорю по-английски.
Technically, you are correct. However, it seems that DL prefers to place adverbs before verbs, and they are teaching us accordingly. This may change over time, and more reports and suggestions are made.
Perhaps a native Russian could let us know what sounds more natural?
Yes, I think so. по-английски means approximately ‘in an English way’, it is a set phrase, precisely like говорить по-укпаински or говорить по-италиански is. However, I suppose one could say «Я хорошо говорю на английский» or «Я хорошо знаю английский», avoiding the говорить по- -и construction.
Technically И and Й are 2 different letters and they cannot be used interchangeably (unlike Е Ё for example, although those are different letters as well but nobody cares for dots above E), so you can't say "англииски". But in my opinion this should be marked as a typo, any native speaker would guess what that means.