Really don't know if that's crossing the line or not, but you should discuss it with your boyfriend.
I wouldn't worry about the "underwear shopping" I would worry more about that she says "he is the closest after my boyfriend".
I would ask her what she means and what she expects from such an relationship.
But if you do, be prepared to listen.
When it comes to the other girl that "want's" your boyfriend. Honestly, if you re reacting to it, you should start ignoring it instead. I'm afraid that instead of taking out it on her, you will take it out on your boyfriend.
My girlfriend had the same issue with me and a friend of mine that became a bit jelous at my gf, because she was my "gf". The other girl sat near me, was flirting with me, and doing stuff in general that my gf found offensive. The more my gf reacted the more the other girl kept prsuing the thing.
There was never a "sexual" thing. It was more like talking more, hanging out and competing for my attention.
I never had a gf before nor did I ever had any reason to suspect my friend for such behaviour, I could hardly believe my girlfriend, and I could only believe her less because she was mad at me and wanting me to cut the friendship.
Eventually I understood and talked to my friend, and told her that what she did was immature and not very wise. She apologised to me, and to my gf.
But my gf has choosen not to forgive her.
Still we meet and my gf has to learn either to live with it, or let it go.
That's simply because I know where I stand. No matter what other girls might have in mind.
And that's the most important thing.
If you trust your boyfriend, then trust him, but don't "protect" him from other girls.
But be sure to tell him how you feel and what you feel is okay and what not. However do not expect that he will agree with you. You'll simply have to comprimise if it's a big problem for you.