I was marked wrong for 'Zawsze on mówi ciekawie' - a correct answer is listed as 'zawsze mówi ciekawie' - do you leave the subject out in this case?
It is about the word order. If you want to put "on", do it in the beginning of the sentence. "Zawsze on" sounds unnatural.
Another word order question: does "On zawsze ciekawie mówi" sound natural?
It sounds even better to my ears. Added now.
Is it because this way we avoid having the adverb at the end?
Great, thank you.
the system hasn't accepted my "On zawsze mowi ciekawie"?
It's exactly the main answer, apart from lack of special character "ó", which is always accepted anyway, just 'with a typo'.
Why doesn't "ciekawy sposób" change to another cause because it is "w ciekawy sposób"?
I think the answer it's that it's a fixed construction.
Also, technically it's not that something is literally "in" (inside) 'an interesting way'.
It is accepted.