When I open the Music D/L app, it quits immediately
I googled a bit and you're not the only one with this problem. It could be that Apple has decided that this app is a bad app. That would explain why it's not available in the App Store anymore and why it won't start anymore: Apple can do that (I think it has to do with the certificate of the developer).

Another possibility would be that you upgraded to a newer version of iOS and that the app is not compatible with the newer version. And for some reason, the developer is no longer supporting the app.

Either way, I don't think it is possible to retrieve your songs. Please don't shoot the messenger.