Songs deleted from iTunes Library after synced into iPhone(5)

Heard a song on my iPhone where, because of the size of my Library, iTunes auto selected about 2,600 songs. Heard a song that I wanted to add to a playlist. But when I went to iTunes Library, it wasn't there. Then I discovered a number (don't know total yet) were missing. How is this possible? Did transferring the songs from computer to device do this?

I have other problems with iTunes: making duplicates, creating new folders, some tunes can't be located so don't play but next or two or three times after re-opening iTunes they resume being able to be played. Don't get it.