Speaker/volume on iPad seems to work but I have no sound on music or videos/etc

Have you tried setting your audio volume from the Control Centre volume slider? Also check the you have not enabled Silent mode as illustrated here:

If you are experiencing difficulties setting the volume of System Sounds independently of your audio volume, try disabling Change with Buttons in your Sound settings:

Settings > Sounds > Change with Buttons

With Change with Buttons set to OFF, your physical volume buttons will only alter the audio volume; the volume of your System Sounds are then fully independent of the physical controls, and changed only via iPad Settings.