You can say "Добраніч / На добраніч". We mostly say it when we go to sleep, but it also can be used for the farewell if it's very late.

I would opt for “бувáй” (bye). There are also “до побáчення” (literally “see you”, but in reality can be used when you’re not planning to meet again in the near future), “до зустрічі” and “побáчимось” (“see you”, and there is a scheduled meeting already), прощавáй (when it’s the last time you see the person). On a side note, “добривечір” is rather a literary version that can be found in books. Colloquial one though is “дóбрий вéчір”. “Здоровéнькі були” is a greeting, not a farewell. it exudes authenticity I’d say :) You can also use various specific expressions to say goodbye, namely: “щасли́вої дорóги” (have a safe trip), “хай щасти́ть” (good luck), “передáй(-те) привíт + Dative (дружи́ні/сестрí/доньцí)” (give my regards to (your) wife/sister/daughter)