Maybe look at a different flooring like Mannington Adura for instance. I would need some more info as to the adjoining spaces.

Yes, self leveling concrete is the way to go and put the floor of your choice over it.

You might want to spend a couple bucks and have the tile tested at a lab. Then you'll know, regardless of whether you actually take it out or not. Vinyl asbestos tile is not a hazard as long as it's not sanded/cut/ground/pulverized. If it is asbestos and you leave it in place just keep that test record with your permanent house files.