I have to keep restarting my iPhone to make Apple Music work

Try to reset your device. This won't delete your data stored on this device.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

Alternatively, you may go to Settings - General - Reset - Reset All Settings

https://support.apple.com/en-us/HT201559

If this does not help, restore your device to factory settings. Note that this will erase the data from your device.

Take a look this Apple Support article: Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support

As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. Keep the Home button pressed until you see the iTunes logo on the screen of your device. After that on your computer you should see the iTunes window saying your device needs to be restored to factory settings. Click on the restore button.

More info here:

https://support.apple.com/en-us/HT201263

If these steps don't work, contact Apple and ask for help.

https://www.apple.com/support/music/

I only had the message about joining Apple Music twice. But tracks stopping (even those, that are made available offline) and library sync stopping happens dozens time a day. Also, the iTunes Store app keeps freezing.

There are some serious issues affecting Apple Music, App Store and various settings on the phone itself. Currently there is no word from Apple about what is required to solve them. Have a look through the other posts on the forum, you'll see you're not alone, which hopefully gives you a little comfort. Even though you say your issue started a month ago, there is a good chance that it's being affected by the current 'outage'.