"Service counter" is a compound noun; it should traditionally be "service-counter," with a hyphen. It isn't "counter-service" because the word-order would imply that "counting" were provided as a service. The idea that the first word in such a construction be an adjective is an increasingly common misconception. Compound nouns are a common occurrence in about all Germanic languages; they are two nouns that, together, form a more specific meaning. It's an easy and empirically-forgivable (compound adjective!) mistake, but a mistake nonetheless.

Yes they do in Australia. It's the counter you go to when you want some help in a department store.

"Service Counter" is a noun and refers to a specific place to go to get help or assistance (such as in a hotel, airport etc...) "Counter Service" is a noun that describes a verb or action. meaning, "to get service at the counter". this is not a common word.