Is this normal??

Ok...Ive been dating this guy for a few months and I know he has a best friend who is a woman. Normally, I think this wouldnt bother me. But he was married to her for a brief 6 months before she decided she wanted to be with a woman (she'd already had three failed marriages with men). Its been 6 years since they went their separate ways and yet they talk every day, often discussing intimate details of their lives and how unhappy she is in her current relationship (big surprise there). She sends him photos to his phone consistently and when we are together she texts him sometimes all day long. He goes to her house to fix things and he meets her for lunch and says he has adopted the role of being a dad to her 14 year old son (none of her exes are involved). She recently had a baby with her female partner and my boyfriend refers to it as "his baby." He assures me he loves her as a best friend but is no longer in love with her, but I am a skeptic. I can't fathom why he needs this connection to her or his sense of obligation taking care of her child if their relationship was so brief. I also am trepidatious telling him too much for fear he will tell her. He says he has told her about me and that he loves me and she is happy for him but one of the first questions she asked him was if he planned to move out of town. She wants him to stay in the area for at least another 4 years until her son goes to college.
I don't know why I have this weird feeling in my gut about this friendship. I just don't think its normal for friends of the opposite sex to communicate every single day. And I think there has to be boundaries. I don't want her to be the one he always runs to if we encounter problems. I almost feel as if there was never any closure. She left him to be with a woman and he never got over her so keeps her as close as he can, almost as a back up plan. Can someone provide some clarity? Is this a normal friendship between a man and a woman or do I have reason to be a skeptic? We spent the entire day together yesterday and he never bothered to tell her he was with me or that he was busy and would text her later. Rather, she texted him literally all day long and he responded, telling me all the drama going on in her life. It leaves a bad taste in my mouth. I love this man. And I want to be with him. But I'm afraid she will be the priority, not me. Someone.....please....provide me with some insight.