Will episodes I play on one phone automatically be removed from other devices?
Generally speaking, yes, which is desired behavior. An episode you play on phone 1 will be marked as played on all other devices, so if you enabled the setting to auto-delete played episodes, it would be removed from those devices too.
You can still choose to keep an episode permanently on your device with a manual download. Also, premium plans introduce a better option for permanent downloads. There are now custom playlists and they come with their own download limit. For example, you could make a "besties" playlist with a download limit of 100 to keep all your favorites offline, even if they're played.