Is there an expression like "Good Nights" in spoken/written English that differs from "Good Night"? People who speak Spanish language use "Buenas Noches" which literally means "Good Nights". The same goes for Turkish "İyi Geceler".
"Good night" (singular) is the idiomatic equivalent of "buenas noches". The origin is from the Old English niht (from the proto-Germanic nahts), rather than the Latin nocte that Spanish derives from.
For whatever reason, northern European languages that derive from German prefer the singular: Dutch Goede nacht, Swedish godnatt, German Gute Nacht, etc.
The Finnish hyvää yötä is plural, however, as is the Russian Доброй ночи. So it seems to vary.
It's not clear why Spanish is plural. The French Bonne nuit is singular, as is the Italian Buona notte, and the Portuguese Boa noite. If you search around, there are many theories why this is the case (also, I may be oversimplifying it, as in these languages it may be correct to use the plural when addressing multiple people)
One possible correlation might be how to tell time in Spanish.
¿Qué hora es? (What time is it?)
Son las dos (It is two)
Anyway, it is possible to use the plural in English, but only as a deliberate way to emphasize that you refer to more than one night.
I wish you many good days and good nights on your journey!
No, in English we just say, "Good night." It's an idiomatic expression, and it comes out of our mouths automatically. We say it without even thinking of the real meaning of each word.