I get the feeling that if I used the feedburner feed, then I'd have more accurate stats on downloads, especially with itunes.
That is possible. There is a unsolved problem with the counter if comes to downloads from the iTunes Store page. If someone plays a media file on the iTS page then the counter counts sometimes not correctly. see http://wordpress.org/support/topic/plugin-podpress-statistics-for-m4v-files-are-not-accurate
With certain settings feedburner seems to resolve the URL scheme which podPress uses to mask the URLs of the media files in order to count and hands over the real URLs to the player. The media players use often more than one request to load a media files completely. Some of them resolve the URL scheme too and use the real URL for all consecutive requests. But some of them don't do that and use the masked URL for all requests. The podPress counter counts every request with an masked URL (and gives back the real URL). That is why the pP counter counts sometimes not correctly.
I think about a way to fix this problem but it might take while.
How do I get the stats from the category feeds?
Under some circumstances (with method Full or if you would use unique media file names) it would be possible to retrieve that information from the stats db table. But podPress has no result page which does that. It is currently not possible.
Can you help me sort out how to get the most accurate stats for all these shows?
Currently something like that would only be possible if you would use the stats method Full. But using that method or Full+ is NOT recommendable if you have a popular blog. These methods don't perform well if you have many clicks.
But these methods store besides other information the ID of the post of the media file and with this post ID it is possible to retrieve th category information. It is also possible the retrieve (post ID and) the category information solely with the file names of the media files. But that would bring only correct results if you use unique file names for the episodes.
Neither of these methods to retrieve the statistic results by category or by category feed is implemented.
But to have separate statistics for each feed is a good idea and when I do bigger modifications I will think about a way to implement something like this. But in the moment I have not much time to work on podPress. So this will probably not be soon.
How do I find how many people are subscribed through itunes?
This is also a very good idea for future versions.