Hi Yevgenia.<<1)Can I get out of my apartment? or get off?>>
Generally, you won't do either. You will normally "leave your apartment" or "go out of your apartment". If you have to "get out of your apartment", it implies a difficult situation. "I can't get out of my apartment! There's something blocking the door!" "There's a fire in the building! I have to get out right now!" "Get your filthy dog out of my apartment right now!"<<2)If a bird escaped from the cage...Did it get out? Or can i say "it got off" ?>>
It got out. Similarly, if someone escapes from prison, or finishes their term in prison, they "get out of prison". <<3) If student sits on the table in the classroom teacher can tell him: get off the table!
I suppose "get out" can not be used in this context...Am I right?>>
Yes, exactly, because in this case, he is "on the table". If he were somehow sitting inside the drawers of the table, you might tell him "Get out of the table!"
Also, be careful with the phrasal verb "get off", because it can have a sexual connotation. If you say "I'm just getting him off the table" it's okay, but if you say "I'm just getting him off," people might start to laugh.
Have a good day.