Translation:Two adults and two children, please.
I agree. O.o
I'd much rather say in Esperanto: du plenkreskulajn kaj du infanajn, mi petas. Now it's strange, ambiguous, lacks the accusative and seems pretty much as a literal translation of English, where adjectives are equal to nouns (or maybe Nominative form is equal to Genitive).
Well, no. If you order stuff, said stuff is object, and gets the -n in Esperanto. Most likely this is a response to a question for a being-state, such as "what size table can I get you?". There are languages that case-mark expressions like these, but Esperanto doesn't, for better or for worse.
If this was a cannibal restaurant in German, they'd probably require some specialized legislation along the lines of the "Rindfleischetikettierungsüberwachungsaufgabenübertragungsgesetz," which means "the law for the delegation of monitoring beef labeling." Such restaurants would probably also need the services of " Rechtsschutzversicherungsgesellschaften," or "insurance companies providing legal protection," which - as I'm told - is generally considered to be the longest word in the German language that's actually used on a regular basis :P