I noticed that for quite a few example sentences the audio does not match the written sentence.
I was wondering why this happens. Did they once match and then only the written sentence was changed?
Is it any helpful to report these instance if I notice them and if so, what would be the best way?
Also I was wondering how sentences (written and audio) are aquired in general. Are they from native material or are they constructed for the app? Are the audios spoken in by native speakers?
Report them as soon as you encounter them. Michael cares a lot about this, and will address issues quickly. You can report them using the in-quiz bug reporting process (tap the (?) button), or by submitting a correction to the sentence (tap the eye next to the sentence), or by posting in the bug forums.
Sentences come from all over and have different origins, but the audio is all recorded by native speakers.
There was a period during which a lot of sentences were re-written to be more accurate for the level in which they were appearing, and the audio was accidentally left unchanged. Sorry about that!
The majority of the sentences came from the Tanaka Corpus, but a large and growing number of sentences (already at 20,000 or so, I believe) were written by native speakers specifically for renshuu.
All audio is, as noted, by native speakers, and done for renshuu.