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What if a song was used once in a placement months/years ago but it's no longer in any library. Could it be submitted to an exclusive listing here?

I would say absolutely, as you still own 100% of the publishing and master at this point and no one else is representing the title.

Yes, if it's not under contract anywhere that should be fine. I had a song placed in a film , direct to supe deal, and subsequently signed that song exclusively and it was no problem.

Yes, but if you are offered a deal by the exclusive library, I would disclose it. Most likely it will be fine but you don't want them to be surprised by something that may concern them.