Light/medium/heavy is the tension of the strings. Vast majority of people use medium, and that will be what you'll need
The set you have on at the moment will be medium tension
Ball and and loop and are the ends of E strings, and which one you need depends on the type of fine tuner you have. I have a loop end fine tuner, but i suspect yours will be ball which seem to be more popular these days - have a look at your E string and see if the end of it is a metal ball or a thin loop of metal on a hook.
A loop end fine tuner will look like this http://blog.sharmusic.com/Portals/47259/im...resized-600.jpg
ball end string like this http://www.swstrings.com/images/education/string-BallEnd.jpg
though the ball may not be hollow
I'm assuming factory fresh means they've just been made and haven't been sitting on a shelf for a long time, not heard the term before though!
So just tell your friend to get a medium set of dominants, she won't know if she needs a ball end or loop end E string till she sees what type of fine tuner is on the violin though unless she asks the shop - i expect it'll be the same as yours
Hope that helps