Q1: what is the underlayment that would need to go in between parquetry/hardwood and concrete ? i guess it would need some sort of a wooden underlayment to which it gets fastened while the underlayment is somehow affixed to the concrete ?
Q2: how much of ceiling height i am looking at compromising by having parquetry/hardwood on concrete ? how about a carpet instead, for the sake of comparison ?
Question 1 isn't easy to answer. There are a few things you have to consider. Is this above or below grade? What are the moisture conditions of the slab? You're probably going to want to lay down some asphalt paper first (maybe two layers) and then you can use either plywood or sleeper, 5/8-3/4" thick. If you're finishing a basement, I wouldn't suggest hardwood of any kind. You're only going to end up with problems.
Question 2 is simple ... how thick is your hardwood? you're probably looking at sacrificing 1.5" to 2". Carpeting would cost you 1/2 to 1" of ceiling height depending on the grade of padding and style of carpet.
Hardwood on a slab....Especially a below-grade slab...Is not something I'd ever consider doing. There are just so many things that can go wrong with the installation down the road. Moisture, slab movement, etc...