1. You have never really worked / You haven't ever really worked in you life.
Yes, they are equal in meaning and also are grammatical. Note that you have a typo, it's your life instead of you life.
2. The director hasn't come / returned / come back yet.
Your three options have slightly different ideas so it depends on what a native speaker want to say to choose one. You would use come here when the director has never shown up. You would use returned or come back (they are equivalent) when the director was there already but he left to go somewhere else but he would come back later.
3. What have you been looking at / examining for long?
Best choice would be looking at in a daily life context, it sounds more idiomatic. But in a more specific context, for example when someone is concentrating on their computer at work, then you could say examining as well.
4. She told me everything when we were coming / going home yesterday.
Both options work just fine. To me, when you say coming home it would be more like that the listener is the person at home, and you're saying to that person that you're coming home to him/her. Otherwise you would say going home but honestly there's not much of a difference.
I don't understand your second question here about replacing both parts, replacing them with what? Please specify the question more clearly.
5. How long is it since he wrote to you last / When did he write to you last / How long ago did he write to you last?
They are not entirely interchangeable, though the ideas are pretty much the same. To answer a how long question, you would give a duration, e.g. a year. To answer a when question, you would, technically speaking, give a point of time, e.g. last year. And to answer a how long ago question you would give a duration of time to go back from the moment of speaking, e.g. a year ago (quite similar to how long, just need to add ago).
Note that for the first question it would be more grammatical to say:
How long has it been since he wrote to you last?
because you use the word since, making the main clause become an action that happened in the past and still at the present.
6. How long is it since you began (not started) learning English?
No, I wouldn't agree so. Both verbs work fine when you talk about learning English. And again, how long has it been would be better.