Depending on context, the first can suggest that her living in the apartment is of limited duration. I moved to a new apartment some two years ago, and can say either 'I live in an apartment on X now' or 'I am living in an apartment iin X now'. I feel no real difference between the two.
At the present moment of calling, I would probably say, "She is not answering my call." After the fact, I would probably say, "She didn't answer my call."
Using "does" falls somewhere in the middle with a slightly different emphasis to my ear. It is grammatically acceptable, but I would probably only say it if I were speaking of this occurrence more than once. For example, "I have ca