Where is the manual for the Apple iPhone Podcasts app?
Is there somewhere that gives more than just a cursory explanation of how to use it?


Probably not - Apple's not big on providing manuals when they don't think they're necessary. 


  For example, when does it chose to download podcasts?


Probably hourly. There's no option to change this that I can find.


  Can you force it to update the podcasts without going one by one and clicking on the download link?


It downloads new episodes for subscribed podcasts automatically.


  Will it download over cellular?


Yep, it does. It also streams over cellular, and well enough that I didn't notice that that was what it was doing at first. (I'm on Verizon 3G.)


  Can it download the podcasts but play through the normal music app?


Nope. It's totally separate. (There's rumor/suspicion that the Music app won't even have a Podcasts section in iOS 6.)