Hello and welcome to Apple Support Communities, AlexRodesc.
If I understand your post correctly, you're not able to download songs on Apple Music from you iPhone. I'd like to help.
It sounds like you've done some great troubleshooting so far. Go ahead and reset the network settings on your iPhone. This will reset your Wi-Fi passwords, VPN, and APN settings. If you use iCloud Keychain, it will also reset your saved Wi-Fi and VPN settings on all devices that use your same iCloud account. Tap Settings > General > Reset > Reset Network Settings.
Once you've reset the network settings, make sure you're following these steps to download:
Download content
You can download content from the Apple Music catalog or from your iCloud Music Library. If the content is not already in your Library, you must add it before you can download it.
To download an item, find it in your Library and look for
near it. Tap or click
to download the item to your device. On your iOS device, when you download an entire album or playlist,
changes to
DOWNLOADED when the download is complete.
Use the Watch app on your iPhone to add music to your Apple Watch.
If you have Automatic Downloads turned on, content automatically downloads to your device or computer when you add it to your Library. You won't see
.
You can download content on up to 10 devices. This content is accessible only when your Apple Music subscription is active.
See the full article here:
Add and download music and video content from the Apple Music catalog
Let us know if that resolves this issue for you. If that does not resolve the issue, let us know if you're able to play any of these songs and if you've tried downloading from a different Wi-Fi network.
Thanks for using the Apple Support Communities. Take care.