Notifications not working with the Overcast app; and is there help documentation for this app?

Funny you should bring up Overcast. I just decided to try it the other day again, and have been using it quite a bit over the past few days. Sped up audio doesn't sound terrible any more. Yay!

Notifications should be working, as far as Overcast goes. I've received a couple notifications last night and this morning about new podcast episodes.

There are a couple of places where you can change notification settings. You can go to Overcast's settings area, and Notifications to quickly enable and disable notifications per podcast. You can also do it when looking at a specific podcast feed.

Otherwise it might be an IOS push notification thing? You may want to use the Feedback or contact link within the app to see if the developer has any ideas.

I have been trying dozens of podcast services looking for the best. Lately I have had Pocket Casts, Overcasts, and the native iOS podcast app running with my podcast library. The topic of which service is best is very very complex and it depends on what features you need, so I won't touch on that here. I will say, however, that with these three apps running on my phone at the same time I can say that Overcast comes in a distant third when it comes to notifications. Pocket Casts has the best notifications by far, alerts seem to come in almost exactily when episodes drop. Apple's podcast app updates at most once an hour, I believe, so notifications go off in hourly chunks, but they do come through reliably. Overcast seems to often just forget that it has new episodes. I will say, even though I find Overcast pretty bad on iOS, it does have one of the better web apps for the desktop.