It sounds like you have a type of gypecrete ( a light weight concrete/cement subfloor material commonly used in multi-story buildings). You cannot successsfully glue or nail to it; So, your options are a floating floor OR a floating subfloor which you can glue or nail to. As far as the stairs, I doubt they are gypecrete as well. Most likely, they are wood. Stairs are very tricky, even for pros. If you want stairs done, I suggest a professional. You may be able to handle the floating floors yourself, if you are very handy.
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