ITunes set to Sync no music, yet there's music on my iPhone

Question

I've been battling this for awhile and got desperate, and yet - iTunes sync does not seem to work as I think it should.
In iTunes I select my phone, and set the Music options to:
"Sync Music" - checked
"Selected playlists, artists, etc." - checked
"Playlists" "Artists" "Albums" and "Genres" all have NO check marks.
On the iPhone 4S:
Settings / Music / Show All Music - NOT Green (message is "Only music that has been downloaded to this device will be shown.").
Sync
I still have hundreds of songs on my phone.
If nothing is checked in iTunes to Sync, and I click Sync, why doesn't it Sync - as in, why doesn't it delete all the music off my phone?
Now, the real problem was that there was one Playlist that wouldn't Sync, or download to my phone.
During the Sync process it kept coming back saying I needed 1.4Gb of additional free space.  (That didn't make sense since all the songs in that Playlist were already on the phone, but no matter).
So I deleted a bunch of Apps. and that didn't free up enough space, or so the message said.
So I tried, via the steps above, to delete all my music, and yet it's still there.
And no, my Playlist, if checked, does not Sync.
One other trivia tidbit - if I check just one song in iTunes, the color bars at the bottom show almost zero blue, for "Audio."  Then if I uncheck it, it shows over 7Gb of Audio.  That seems backwards and nonsensical.
So, in order, my "needs" (request for help):
* How do I get a playlist to show up on my iPhone?
* Why does Syncing. with the options above, which should delete all music from the phone, leave all music on the phone?
* Why would checking one song in iTunes show that a little space would be used by Audio, but unchecking it (leaving all boxes unchecked) show over 7Gb of Audio would be there?  (See question above - there's nothing checked, so it should be zero, right?)

Answer 1

Music can end up on your iPhone in different ways, not just by auto-syncing.  For example ...
iTunes purchases made directly from the device.  These can remain on the iPhone even after you sync to your library (which should copy them from your iPhone to your library).  Purchases made from the iPhone can remain in either of two ways I've seen -- a "Purchased" playlist that automatically gets created and the songs remain on the device until you delete the playlist and its contents (either right from the iPhone, or via iTunes).  But sometimes there's no such playlist and these purchases remain in a "Manually added" state.  If you look in iTunes where you set your Music sync settings, scroll to the bottom of that window and look for a "Manually added items" category.  It will only be there if such items exist on your device.  If you see this, select all items in this category and delete them, then initiate a sync.
As a variation of the above, if you ever did have "Show all music" turned ON and tapped a cloud, those items will be downloaded and can act like new purchases as described above, where they may end up in the "Manually added items" category.  If you don't see them in this category, just for kicks turn "Show all music" ON and download one song from the cloud -- you may then see that song, and perhaps several others in your "Manually added items" category.
Another possibility -- even if you auto-sync you can still manually drag and drop music from your library to your iPhone.  Such items end up in the "Manually added items" category described above.  If you see these, select and delete them, then initiate a sync.
As a final suggestion, you may have to do what I did -- temporarily change your iPhone to "Manually manage music and video", then Apply the change.  Then navigate to your iPhone's contents while connected to iTunes.  If you see music on the iPhone, select all songs and then delete.  But, you're not done -- to really make this stick, perform a backup to iTunes while your iPhone is still in Manual mode and empty of all songs.  Then Restore the iPhone, load your backup back in place, which should then put your apps back on -- and no music.  Now change back to auto sync, select your Music sync choices, then start auto-syncing.  Hopefully that nukes the rogue songs for you ... it did for me when I first installed iOS 7, and then again after doing an iOS update.