Solid Hardwood, Engineered and Laminate Flooring - firebreak between floors

I am putting ceramic tile in a condo on the third floor. On top of the subfloor is a 1/2 inch of a plaster looking stuff. From previous posts I have been informed that this is not suitable to tile on. So I went out and bought 3/8" plywood @27.00 each(ouch), even though I live in BC were they mill the stuff. Anyway, I have 2 questions #1. Upon removing lino the paper part stayed on the floor in most spots. The spots were it lifted the adhesive took a layer of this plaster stuff with it, thus floor is uneven. Do I just apply floor leveling compound on floor then plywood or what or do I have to get rid of 1/2 inch of this stuff (messy or what)? Question #2 If I do put plywood on top of this plaster firebreak stuff do I glue it or screw it. Me thinks this stuff is no good? Any help would be much appreciated seeing this has to be finished by Christmas.