After reading your last post, I can now see why this bothers you so much. But! I still think it has more to do with you struggling with insecurity than your boyfriend doing something wrong.
I don't think you should be concerned about other people flirting with your boyfriend, as long as he doesn't flirt with them. If someone has feelings for him that is out of his control, and if it's a friend it can quickly become very awkward if you confront them about it, so maybe he doesn't let it bother him because it's easier for him to just ignore it? In the past, I've had someone I thought was a friend flirt with me and even ask me for nudes. Back then I did not know how to handle this at all, and I didn't really think of it as flirting until he started asking me for photos all the time, so I just tried to ignore it whenever he'd ask and just talk about something else (yes, it was really awkward, haha).
If someone sends him naked photos without him asking for them though, that is sexual harassment. Also, The friend who talked badly about you behind your back sounds like a very jealous person, and while I agree that it is annoying, people like that are not worth a moment of your time, so you really shouldn't worry about her at all!
Now, let's say that this woman he is currently talking to actually has feelings for him, how is that an issue? Her feelings are not you or your boyfriend's problem. Her having feelings for him does not mean he has feelings for her. It seems like you are very focused on your boyfriend's friend, as if she will ruin your relationship somehow, but if your boyfriend did cheat or leave you or something like that (I'm not even sure if this is what you're worried will happen) then that would not be the friend's fault, but your boyfriend's own choice. So the problem then would be your boyfriend, not the friend.
If he's the kind of guy that will flirt with anyone, cheat on you and leave you for any woman who shows interest in him, then it doesn't really matter who he's talking to because it's his personality that is the problem. But if he's in love with you and not interested in anyone else, then someone being in love with him is not a problem. It will not affect your relationship in any way.
I also don't think it's fair of you to know about their conversations. That's private and between them, not because he is hiding something but because having someone as a fly on the wall is very uncomfortable and if it was me I would feel like I was really disrespecting my friend.
Again, you are very concerned about his friend, but she's not really the issue here. You not trusting your boyfriend is. Is there a reason you don't trust him? Has he done something that broke your trust in the past?