https://www.google.com/search?client=firefox-b-d&q=%22каждую+отдельную+ночь%22

This just means absolutely every night. “It’s nice to have the neighbors drop by once in a while to say hello, but Harry comes over every single night right around dinner time.”

каждую ночь без исключения (?)

Yep

“Single“ is just the word that we used to emphasize “every“: Grumbler came over with seven of his friends and I knew every single one from school.

Grumbler, SINGLE here means единый, not отдельный. Would it be possible to emphasize EVERY NIGHT in Russian as каждую единую ночь? : "I know you like Millionaire, but do we have to watch it every single night?"

👍🏼🤩

Grumbler, SINGLE here means единый, not отдельный. Would it be possible to emphasize EVERY NIGHT in Russian as каждую единую ночь?

OK, удалил.
Другого способа to emphasize, кроме моего второго перевода, я не знаю.

Каждый божий - вполне возможно - https://context.reverso.net/translation/russian-english/каждый+божий+день