How do I get my multiple podcasts to automatically play successively. I have them download automatically. But instead of playing the next podcast in the list - it plays the older episodes of the same podcasts until I change it.

Yeah, I've noticed that as a quick some time ago. I created a smart playlist, "unplayed," in which I have my unplayed podcasts aggregate instead. Seems to work well in nearly all cases. I have noticed a quirk that if I have a played podcast, connect to car play, ask Siri to play podcasts, and if the played podcast starts again, it then just plays the show in sequence, not the playlist.

You may also want to configure limiting episodes. It's not necessary but over the years I've suddenly received every episode in the feed (usually when the podcaster change the feed location or edits their directory file). To prevent that, I limit episodes if it happens. It's then just a quick refresh and it ensure that you don't get bombarded with older episodes.