The adhesive emulsifies with water. Therefore you probably have a leak somewhere.
I presume the tiles will just peel up. If they do then scrape the emulsified adhesive off the floor and check for damp.
If it's solid it should be nailed or glued down so underlay is not necessary unless for extra sound proofing.
Have you considered the possibility that you may need, in the future, access to the floor - pipes underneath/ cables to lights in rooms below etc.
I would suggest perhaps a click...
What you have is a laminate floor (presumably over an underlay) over vinyl tiles (probably containing asbestos) over bitumen over concrete.
The chances are there will be no dpm in the sub floor.
If you are going to put down sheet vinyl it will need to stuck to the sub floor, cushion vinyl...
If the asphalt was level why did you degrease, prime and screed - I don't quite see the purpose of that?
You would only need to do that if you were sticking down the wood to the concrete, otherwise it's just a waste of time and money sorry.
You would not need another dpm over the asphalt.
The thickness of the Elastilon will be approx. 4mm so that should raise your floor level by the required amount.
If you want it raised by an additional 4mm. then you can screed but you would need to check with the manufacturer of the...
I would ask the adhesive manufacturers if their product will be ok with the asphalt, rather than rely on the word of the asphalt people.
I would not adhere a solid wood floor to asphalt again myself, I would use one of the two methods I mentioned.
If it is as thick as you say it sounds like asphalt.
It is possible to use an isolating membrane over the asphalt that will allow you to glue down a solid wood floor.
However, there is a possibility that if the wood moves then it can pull the asphalt as the asphalt is not actually bonded...