Is it harmless to see your boyfriend with his arm around his best female friend?

It could be a subconscious sign of attraction. Of course, she could just be nervous, or bored, or ... . If you act jealous, that will generally not prevent him from pursuing her, if that's really what he wants to do. On the other hand, if you play it cool, they will probably just stay close friends and not think of each other in a romantic way (even if you feel jealous inside). So, keep an eye on him for the sake of protecting your own heart and feelings, but recognize that there's not much you can do if he really wants someone else. Your philosophy should be that even if this guy leaves, it's no big deal, as you can find someone as good (or better) with little difficulty. Then he will subconsciously perceive you as being worth keeping, and will work harder to win you over.

Of course, you *do* have to put forth the effort, so that you are a great catch worth winning over.... otherwise, he will eventually figure out that you are all sizzle and no steak. ;-)

I would cut this off at the ankles right now. If shes running her fingers thru his hair? She shouldt have her hands on him, especially if she knows he's taken..shes asking for problems

Could be harmless or it could not. Depends upon the person