Okay, her behavior is a LITTLE inappropriate. I do believe that girls and guys can be friends, and yes, even with exes. But my ex who I am still friends with, I only talk to once every couple weeks. It would be fine with my bf if I got a job with my ex, because he's cool with us being friends. As far as this one guy goes who she talks to all day, every day, this might bother you, but yes she is allowed to have friends. Personally, I wouldn't want my man talking to another girl every single day, and he would respect that, and relax with it. All you can really do is express to her that you uncomfortable, and if she doesn't care, then she doesn't about you that much. Express to her (in a mature manner) that she is allowed to have freinds (obviously) but you are uncomfortable with the fact that she is talking to this guy every day, all day. Maybe set some ground rules for the time you guys spend together!
May the wind always be at your back and the sun upon your face. And may the winds of destiny carry you aloft to dance with the stars