Adding MP3 audio into Logic Pro X messes up the audio and chops it.

This is a well known issue with MP3, Logic and Catalina.

A workaround is to convert to an uncompressed format. Wave or AIFF.

Few users reported that recent Logic versions fixed the issue. Current version is 10.5.1.

WD

Without a doubt the alternative solution to convert to an uncompressed format is the best, you can try https://en.savefrom.net/9-how-to-download-facebook-video.html , since this unsolved problem of Logicv and catalina