If you are a young female traveling alone you will likely not be comfortable staying in the Termini station area. You might look in the area around St. Peters instead.

Its been a very rainy season thus far so it is hard to say how the weather will be in February. You shouldn't expect snow/freezing temps but you'll want to bring a sweater, pants, etc..

Be aware that in off season many museums are only open in the morning so you will want to plan your sight seeing accordingly.

As for what to see/do, where to eat, etc... there are numerous threads in this forum and a search of Rome should provide lots of ideas.