Moved to InDesign EPUB forum.
So, I figured the first question out myself. It's resolved here.
The second question remains:
Can I make an audio-clip continue after page turn?
I found the "Stop on page turn" - but it doesn't seem to work. It's not clicked and the music still stops on page turn. I've tried both options, and it doesn't change anything.
It could be EPUB reader specific. What EPUB reader are you using to view?
I've tried a few different readers, but I'm building this ebook specifically for iPad, so iOs 8 and iBooks, newest updates applied.
Audio clip playing on one page cannot be continued after page turn. One workaround could be to add another audio on next page and mark it to auto-play but of-course it will play from start and not in continuation from previous page.
That's what I thought. Thanks for answering!