Some songs got renamed or put under a different artist, because I guess, the actual song is not in the MusicBrainz database
How did you manage that? If picard can't find a song, it won't put it in the rightmost view and it won't be processed.
I don't let Picard move my files, only tag and rename them, because (last time I tried) I couldn't easily see where it was going to move the files to verify if it's correct. I run Lidarr pretty much exclusively to sort everything correctly lol.