How do I add a podcast? Tap + and type the show's name to search, or paste its RSS feed or Apple Podcasts link. In Safari you can also tap Share, then PodPlayer.
Can I play my own audio files? Yes. Tap + then Import Audio Files, use "Open in PodPlayer" from another app, or drop files into PodPlayer's folder in the Files app (On My iPhone, PodPlayer) or from Finder on a Mac.
Where are downloads stored? On your iPhone only. Settings shows how much space they use and can delete played downloads.
A feed won't load. Check the link opens in Safari. Some sites publish their feed at a separate address; pasting the site's main page often works too, since PodPlayer looks for an advertised feed.