This app was mentioned in 18 comments, with an average of 1.72 upvotes
Tunein Radio has a record function. I haven't used it myself, but it sounds like it should work for what you want.
It has gotten rather expensive since I bought it. Here is a free alternative.
This app does sound interesting, currently I'm using this app: https://play.google.com/store/apps/details?id=com.audials as my main app. Also I still have this app installed: https://play.google.com/store/apps/details?id=com.finallevel.radiobox
I've decided to go ahead and give this app a try.
https://play.google.com/store/apps/details?id=com.audials
Not intuitive at all but might work. Add url in settings. Play station select record continuous. Then go in settings (3 dots) and features (looks like a heading not a selectable button to me) scroll to background /scheduling recordings and change your schedule. You may have to poke around a bit it is a beta.
Edit: clarification
I've recently been trying out Audials.
Free to download, no ads (outside of the radio streams themselves) and it includes a recorder. Drawbacks are that the connection can be kind of flakey and it looks kind of ugly.
Not sure if this fits all your requirements but you can manually add a URL to Audials (https://play.google.com/store/apps/details?id=com.audials). And it supports Chromecast
Audials works for me. No ads and has a lots of stations with regular updates. https://play.google.com/store/apps/details?id=com.audials
Hi,
These two apps will help you get what you're looking for.
Audials is a free internet streaming app similar to all others, but you can record while listening, or scheduled recording in the background. This is a real gem, covering every genre. Available on most platforms too, nit just Android.
https://play.google.com/store/apps/details?id=com.audials
This app, available from xda developer's, (not playstore) but safe, free, ad free, open source, let's you download mp3 from YouTube. Covers many other formats too. But, I used it just for music downloads.
https://labs.xda-developers.com/store/app/dentex.youtube.downloader
And to play all music, this is one of the top players in playstore. There is a trial version, but the paid, or pro version is only a few dollars. We'll worth it. But, all phones have native players, and most third party file manager apps have built-in player's.
https://play.google.com/store/apps/details?id=com.maxmpz.audioplayer
I like Audials Radio Player https://play.google.com/store/apps/details?id=com.audials
Plug the stream into http://streamripper.sourceforge.net/
Also check out https://play.google.com/store/apps/details?id=com.audials&hl=en
Give Audials a try. It has all of my favorite tunein streams. I prefer it's interface now. Tunein in has been flakey for me as well.