If I update a podcast episode on my server, when does it get updated on Apple Podcasts? I have noticed that some podcasts are different depending on the date I download them. For example, some have different advertisings when I download them again. I also noticed that some podcast episodes are no longer available.
So I suspect that podcast files live on the publisher's servers and Apple Podcasts does not host or cache them.
Is that true? If I update a podcast episode on my server, will all downloads after that get the new version?
Apple hosts a directory, Apple does not host the files of podcasts.
If you update the file of a podcast on your server, but do not indicate that you've updated it in your RSS feed, then only new downloaders will get the new file (obviously).  If you update your RSS feed to indicate that there is a new file, then many podcast catchers will figure out they need to re-download the file.  Others will simply list it as a new file again.