Kałasznikow otworzył sklep z pamiątkami na moskiewskim lotnisku . Just in case you need an AK47 to go with your duty free wodka before your flight...
In your English sentence, you know that there is some specific shop, and you ask where it is located. The Polish sentence asks if there is any shop at the airport.
"ma" = "he/she/it has". It is used in such constructions, but negative ones. Not positive and not questions. So "There is no shop at the airport" would be "Nie ma (żadnego) sklepu na lotnisku".
żadny is a word that is not noted by dictionaries. The proper for of it is „żaden”. But even then that wouldn't make a proper sentence. This meaning of „any” is usually translated as: jakiś/jakikolwiek/jakiś w ogóle.
If it helps you „żaden” is similar to the German „keiner”: keiner von uns = „żaden z nas” = none of us (man)
And to the second part: yes your proposition is reasonable. „Czy ten sklep jest na lotnisku” or „Czy sklep <Name> jest na lotnisku”.
Because you don't know anything about any store. You know that there is an airport. You ask if there is a store there.
I have to say though, that the Polish question sounds a bit odd to me. I'd rather ask "Czy na lotnisku jest [jakiś/] sklep?". I will see if other team members agree with me.