I used to spend a lot of time on a web site called "Garden Web" and there was a guy in there that refinished hardwood flooring for a living. What I'm telling you in here is what I learned from him. He didn't post under his real name as I do, and he quit posting on the Garden Web site anyhow, so I know of no way of contacting him directly. However, I'll outline the problems you face the way I see them, and maybe you can just contact some hardwood flooring contractors through this website to discuss the problems with people more knowledgeable than I:
I think your best bet is to find out what's on the parquet flooring by seeing what removes this old wax. Back in the 1950's and 1960's, before polyurethane became the hardwood floor finish of choice, people use something called "Carnauba Wax" (made from the Carnauba palm trees of Brazil, and still sold as a "car wax" or car "polish"). The problem is that Carnauba Wax isn't very hard, and that means that dirt gets embedded in it easily, and I expect the heat of the Sun in your area also softens the wax and makes it even more susceptible to getting dirt embedded in it underfoot.
The problem I've heard is that Carnauba wax will penetrate into the surface of hardwood flooring, so that even if you remove the old wax, a new coat of polyurethane won't stick well to the wood because of the wax in the surface of the wood. The problem is that the Carnauba Wax in the hardwood interferes with the adhesion of the polyurethane to that surface and causes something called "fish eyes" to appear in the polyurethane (which I've never seen). I've been told that the only way to avoid that problem is to sand down the surface of the wood to remove the wax affected surface layer.
And, that brings up the second problem. I'm no hardwood flooring expert, but my understanding is that you can't just use an ordinary hardwood flooring drum sander to sand down a parquet hardwood floor. The reason is that the wood grain is going in different directions. One option is to use an orbital flooring sander, which is really just a normal palm style orbital sander on steroids. Instead of weighing 4 pounds, it weighs in at about 140 pounds instead, and has commensurately more power.
However, this web site suggests doing the sanding with the smaller handheld power tools; using a palm orbital sander around the edges and a 3 or 4 inch belt sander for the middle:
Finally, the idea of using polyurethane warrants comment. Polyurethane has inherantly poor resistance to UV light from the Sun. I expect that this could be overcome by adding sufficient UV blockers to the polyurethane, but you'd be taking a risk just using any hardwood flooring polyurethane outdoors in an area like yours. You'd have to find a polyurethane that was both meant for use on floors and OUTDOORS, and I don't know if you'd find such a thing. I think your best bet to find something suitable to refinish with would be to contact the places listed under "Janitorial Equipment & Supplies" in your yellow pages and find out who sells S. C. Johnson Wax products. The company who's sales rep you actually want to talk to is called either JohnsonDiversey or Johnson Wax Professional.
Google finds that web site, but can't get to the page for some reason. The janitorial supply places that sell Johnson Wax products will know who the local S. C. Johnson Wax rep is in Abu Dhabi.
Also, you ought to know that finding a suitable finish for wood outdoors is a problem in North America. That's because wood swells and shrinks with changes in it's moisture content caused by seasonal changes in humidity. In order for a coating to stretch and shrink with the wood, it has to have some elasticity, and that requires that it have some softness to it. However, to stand up well on a floor, you want the coating to be hard as possible so that dirt doesn't get embedded in it underfoot so that it starts showing wear quickly in the traffic lanes. The requirement that the floor coating be both soft enough to stretch and shrink with the dimensional changes in wood AND be hard enough not to get dirt embedded in it underfoot is why you simply don't find any actual coatings meant for decks and outdoor verandas in North America. Instead, people here just treat their decks with a stain that contains a water repellant. That just keeps the wood dry so that it doesn't rot. Where you live, there might not be enough of a change in humidity from season to season to have a problem with wood movement, I just don't know.
The only alternative I can think of that might work would be to use an exterior oil based paint, a "deep base" which is intended to have a lot of colourant added to it, and just don't add any colourant. Such a deep tint base would dry transluscent, not clear, and that would not be desireable on a hardwood floor where you want to see the beauty of the wood.
See if ammonia removes the finish. If so, it's Carnauba wax. See if paint stripper (methylene chloride) removes it. If so, it's probably real varnish, or maybe polyurethane. It might also be shellac, in which case alcohol (denatured) should remove it. It might even be an acrylic finish meant for vinyl floors, so try some "floor wax stripper" meant for acrylic floor finishes. A good one that I like is a product called Revelation made by the Buckeye Company, but any stripper meant to be used on acrylic floor finishes should work on an acrylic floor finish. The first order of business is to find out if it's Carnauba wax because that will determine whether or not you're likely going to have to sand the floor down prior to refinishing.