A playlist is a reference file that tells the location of the song. But if you move the location of the song after you created the playlist, then the playlist won't work. That's why you get the broken links message. The songs aren't where the playlist says they are. In future, move your songs to a music folder where they can permanently remain. Then add them to Musicmatch.

For downlding, choose files from the search results that have 3 or 4 stars & have many sources listed under the # column & this will greatly improve your chances of successful downlds. Also try not to downld too many at one time. Otherwise they may queue for some time & in the meantime the original sources may go offline.