IOS – What does “Add to Library” and “Remove from Library” mean in Podcasts

You say that sometimes you "forget" to sync. Are you utilizing Wi-Fi syncing? The sync activates whenever you're on the same network and your device is plugged in. This might reduce the number of instances that you need to download a copy from your iPhone.

I realize this is a stop gap. I feel your pain. Like you, I've put a lot of effort into understanding why the leading podcast catcher can't seem to make podcasting on the iOS "just work". In the end I needed a bit of self inflicted tough-love and just admitted that this was one are that Apple fell short and that they weren't going to remedy anytime soon. They're putting their resources where the revenue streams are.

My situation forced me to change my workflow. I've been waiting for the promise an untethered world, and jumped into iCloud full steam. I use iTunes Match for my music, iCloud for my backups and no longer sync to iTunes on my computer. Of course, this means that there is no way to subscribe to podcasts on my iPhone without using a third party app.

After trying several podcast apps, I've come to like both Downcaster and Instacast. I've imported my feeds from my mac, I can subscribe to new ones on the iPhone, and I can sync to my other devices through iCloud. What I can't do is sync back to the mac. But I'm ok with that now. By using a full featured app on the iPhone, I've come to really like the experience. Given the choice today, I'd continue my new habit of listening to podcasts on my phone even while I'm working on my mac. I don't ever need iTunes open and the overall listening experience is much better.

I'm not sure about your first question. I suspect that Keep Most Recent refers to the most recent in the feed, but I don't know for sure.

As for the second question, the Podcasts app adheres to Apple's rules about background/scheduled downloading. That is to say, it only checks for new episodes when the app is open. This is a power and performance optimization decision, and for better or worse, no third party apps are allowed to schedule background checks either (although in theory they could on a jailbroken device, but I don't know if there are any apps that do this). Apps can trigger background downloads using geofencing however (the same way Reminders can trigger an alert when you leave your office).

There are several other podcast apps on the App Store, which have finer grained controls for subscriptions, and so forth. Downcast and Instacast are likely the two most popular ones.