I'm certainly not one to give you all the answers on this since it especially involves a NYC apartment. BUT, I'll try.
One thing is she needs to be sure what she has for flooring currently. If it has a lot of 'flex' in it, then the parquet will flex too. What you most need to look at is 2 things. 1) Assuming the current floor can 'accept' parquet right over top of it, how high will it raise the floor? Will the bottom of doors need to be cut? 2) Assuming she'll need to put down 1/2" or more underlayment BEFORE she install the parquet, will there be TOO much height such that the transition between rooms is too high?
One thing I look at first is to see what it would take to get down to the 1st layer that will 'accept' what I'm installing. Again, this may NOT involve removing any of the existing flooring. Then, I lay down a piece of wood at EACH doorway, room-transition, closet, stairway, etc., etc., and see how things will work (or not work) with the new flooring. IF there are any problems, one needs to consider removing 1 layer of existing flooring at a time until you get to the NEXT layer of existing flooring (or sub floor) that will accept the parquet. It's sort of a building-of-layers process. I just installed some hardwood in a foyer and had to remove 1 layer of parquet and 1 layer of vinyl+underlayment. That's about 3/4" of flooring. This allowed me to install the 3/4" hardwood right on top of an 'old' layer of vinyl+underlayment (which was on top of a 3/4" sub-floor, which was directly over floor joists).
I know a lot was said but you may want to get an estimate or 2 and ask the contractor what they'd do, then go from there. At least you'll be informed of what THEY'LL do to install your floor. As for tools to do his job yourself, you'll need things like a chalk line, the mfgr's suggested glue trowel, the proper glue, most likely a power miter saw (to cut the parquet), and some patience. My best to ya and hope this helps.