'She lives on the same floor as me' is fine. A strict grammarian might tell you that 'She lives on the same floor as I' or 'She lives on the same floor as I do' is more correct, but we don't tend to say either of those. These days we would all say exactly what you said : 'She lives on the same floor as me.' You would only use 'mine' if there were a possessive construction involved, for example, 'Her address is the same as mine.'

I think that "She lives on the same floor as me" is technically a bit incorrect (if someone knows the exact rule let me know), but is very commonly used in conversation. "Mine" would be incorrect. Other more grammatically correct ways to say it would be: "She and I live on the same floor." or "she lives on my floor." Again, if you are just speaking in normal conversation, the original sentence is fine.

Both are correct, but "as me" sounds much better.