Figuring out Podcasts App iOS7

The SSL security problem forced me to become acquainted with the Podcasts app in iOS7 on my iPhone4 and iPad. I was content with iTunes managing my podcasts--it wasn't perfect in a few ways, but it was highly functional. I've been managing my podcasts and keeping a perpetual playlist in iTunes (all unplayed non-video-podcasts with two sets of sorting lists so that they the oldest ones played first, mostly, but also some randomization thrown in) that worked very well to sync to all my devices, and I could do a quick plug-in & sync when changing from playing my list off the computer to the phone .

Now iTunes says it will use my Apple ID to sync podcasts and podcast playlists between iTunes and the phone, and I can still access my podcasts from both devices, but the syncing is far from seamless, and I'm trying to nail down some of the details to understand why.

For example, I was listening to a podcast tonight and playback from the phone over Airplay was haltingly slow. I noticed that there is a 'download' icon next to the title of the podcast on the playlist on the phone. Does iTunes default to streaming instead of downloading the podcasts? Especially for this use, I never want to be dependent on streaming to listen--I spend a lot of time mobile while listening to this list on the phone, and need things securely there, downloaded when I have a good wi-fi connection or synced from iTunes on the computer. Can I force this?

And more: is the 'sync' via the apple ID simply recording where play was stopped on any particular podcast, or is it syncing what is downloaded and what is deleted? Does it 'sync' when something is deleted on one device without being completely listened to?

And does iTunes on my computer communicate anything to the Podcasts app via USB sync if internet service is not available?

I'm on Mountain Lion (10.8.5) again on the laptop, because I like USB sync and can't use the cloud for enterprise security reasons.

Googling and quick searches here have not been helpful.