"Hello" is fine for all occasions, even "hi" is almost always acceptable (that is, it's normally OK to use even when you are talking to someone in a formal situation).

"Good morning/afternoon/evening" would generally be considered a little more polite and respectful, but any of these greetings can be used more-or-less interchangeably.

I sometimes say "hi" to my bosses and lecturers, and I also sometimes say "morning" or "afternoon" (the word "good" is often omitted in informal situations) to my close friends.

I think the rules regarding formality/informality are much less rigid in English than in Russian.

edit: actually, if you're talking about written communication here, don't use "hi" as a formal greeting, use "hello" instead.