Why are my iTunes songs going missing from playlists on iPhone?

Hello folks...

Anyone have any idea why some songs have simply decided to leave my iPhone?

I bought them, put them into playlists, and recently realized that I hadn't heard them in a while. So when I went to look for them, they were not to be found. However, I could redownload them free of charge.

WHAT THE HECK??!!??

I do not have an iCloud account, but I did back up my phone recently through the Finder. Maybe I set something incorrectly?

Secondly, I have found many songs on my iPhone that I never downloaded -- nor would I ever.

Can someone out there explain what the hey is going on?

Thank you.

[Re-Titled by Moderator]