Re: Leveling a damaged Vinyl Composite Tile floor in order to paint it.
Why would you purposely try to patch a floor that is beyond it's useful life? I would recommend tearing it all out, down to the subfloor, repair any subfloor damage, install new underlayment, then install new vinyl (solid surface, not tile ). None of this is particularly difficult and you will have repaired the floor properly, not just put a bandaid patch on which will stick out like a sore thumb.
As for the presence of asbestos, you can take samples in for testing (it's usually in the glue ), then decide what to do. I personally wouldn't be too concerned about it, just use care as you remove the layers of flooring.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!