In formal/polite Korean there are also 2 expressions: 1) 안녕히 계세요 (If you are leaving, and the other person is (or the other people are) staying) 2) 안녕히 가세요 (If you are staying, an the other person is (or the other people are) leaving)

You can use it in both cases, but keep in mind that 안녕 is the shortened, less formal form of 안녕하세요 just as "Hi" and "Bye" are shortened, less formal versions of "Hello" and "Goodbye." :)

yes it can be used in both cases :-)

Yes it can be used in both cases and others are correct in saying it is basically a shortens version, importantly, there is also a difference in putting accents. Usually, saying hi goes: 안→녕↑ and when saying bye: 안→녕↓