I know the two other popular ways to get podcasts are with Canola (but I really dislike the way Canola manages podcasts) and bashpodder (which is CLI and sort of a kludge, requiring a little bit of coding knowledge and just plain seems plain unweildy for any ordinary user when things don't go 100% right).
Yes! In gpodder, to go the drop-down menu and choose 'Podcasts' then 'Preferences' and remove the checkmark beside 'Show icon in status area'.
Hmm... that's not a behavior I've seen at all. Maybe try this: Go to the drop-down menu, choose 'Podcasts', then 'Preferences' and tap 'Advanced...', start entering in the word 'mini' and make sure there is no checkmark next to 'minimize_to_tray'. Tell me if that works either way--I'm curious about that one, since I'm not seeing it at all.
Actually sounds pretty good over here--I've preferred using it with Panucci ever since I started using it. I also tend to use bluetooth as well as speakers and headphones and I'm not noticing any difference in quality except the obvious degradation in quality from using HSP profile bluetooth audio, which is to be expected.
I'm not sure I understand what you mean. If you mean tha you don't want them to be able to be deleted, there is a menu option to mark an episode with 'Prohibit deletion' so that it won't be able to be deleted and it remains available. If you mean that you want to be able to archive episodes elsewhere by saving them off, you can tap an episode and choose to 'Save to disk' which lets you save the file off onto another card or a specific path (say SMB).