Hi,
I have had the same issue. not being able to add individual songs, unless i did complete restore.
this was on ios6, and ios7.
This is my solution.
Total of 4 Steps
Step 1 - (this portion only needs to be done once.) go to the bottom right in itunes, open settings, drag scroll bar to a few hundred megs, and select box choose items randomly., click ok.
Step 2 - drag the songs you would like to sink up to, into your Music library ( on the left hand collum, Directly over the Music Library .
Step 3 - Choose your library in Autofill forms ( in my case its the default; Music)
Step 4- press Autofill , you will see the syncing icon go from grey to black next to each song.
it worked for me
As for Where your back up's are. I would assume it is in your itunes media folder location. ( that is where mine are)
Ussually in \user\ mydocuments\music\itunes, in there you will find your apps, music, etcs
Note: i deAuthorized all itunes licenses on various computers, . i had six licenses. max licenses allowed by apple is five. I authorized my itunes on my windows8.1 pc. wether this step had any effect or not; i do not know.
Cheers🙂
Marc