Can you and how do you melt quark cheese into bechamel?
Quark doesn't melt at all. What you can do is to stir it into the sauce. 

From there on, it depends on the version you have available. I haven't seen the Polish one. If it is firm and crumbly like some of the quarks I've had, it will remain that way in the sauce, and you will have a grainy texture. The German type is similar to yogurt in texture, and it will blend with a sauce perfectly (but not melt). Polish cuisine borrows from both Russian (which has firm quark) and German (which has the aforementioned yogurty quark) so I can't predict what will happen with what you have. 

Note that having a somewhat crumbly texture in a sauce is not necessarily a bad thing. Personally, I like a lot a sauce/dip made from 50% mayonnaise and 50% firm quark, stirred together and served with black olives. It depends purely on your taste. My advice is to make the sauce and see if you like eating it.