Some songs from forum playlists do not appear on main song list

[dflat]

What should be happening is any imported song or playlist will import and then list in the Songs index (except for any duplicates) automatically.
If this occurs again, you could look at the smart playlist "Last Imported" (with large playlists, it will not list all the songs imported)and check various songs have registered (listed) as being imported.
Yes any new songs having been imported should then be able to be Searched for and listed.

Reinstalling the app might clear it, if it is some kind of corruption within the app. You could run a backup (making sure all the songs you use are actually in the app (if you have a spare device, you could import the backup and double-check all your songs and playlists are there), then trash the app and download it from the Playstore (it will be free), then import your backup.