I suppose there’s already a number of suggestions addressing those various features…
- download playlist for backup → duplicate
 Export music playlist to m3u+media
- download entire library/all playlists to plexamp → duplicate
 Download entire library or playlist in Plexamp
- share individual playlists w/ other users → implemented
 Single Item Shares | Plex Support
Not aware of an issue where playing a playlist stops after 4-10 songs. That sounds more like an issue/bug…