Hi Elmima,
Thanks for posting! It sounds like you have issues with Apple Music skipping the end of a song randomly and missing some album artwork. Nice work trying to re-authorize your computer. We'll do our best to provide solutions to both issues.
To address the issue with the album artwork missing, try to right-click or Control-click on the song in your library, then select 'Get Album Artwork'.
For the songs skipping the end, that's harder to address. Are these songs downloaded or being streamed when this happens? Does this happen when you are using a Bluetooth device to listen to the music on the Mac? As you move about and out of range of the Mac, it may skip or pause while using Bluetooth devices.
Are there any similarities with the music that skips? For example, is it the same album or occur around the same time each day? Have you tried to re-add the content to your library? If not, here's how to test that out: Delete music, movies, and TV shows from your device and Add and download music on Mac
Hopefully these suggestions helped out, if not reply back and we'll continue to assist. Cheers!