Sync problems are often caused by user inexperience with the editor.
If the music is a separate track from any video clips (UNlinked), then right-click at the left of the track and lock the music track. (If it's linked, right-click either the video or audio track and UNlink it.) Then video can be edited without affecting the music.
Of course. Save Project File AS routinely, giving it a unique # or name, so as not to overwrite prior saves. Using Save Project Files (no AS) will overwrite. Then you can restore a project to the state it was in when saved. Just double-click the VPJ file (which isn't playable). And if you make a mistake, press <ctrl-Z> to back track, step-by-step.