You have already told him that it bothers you and still he will not stop talking to her he may like the attention that she gives him and the fact that he doesn't consider your feelings about this issues shows me that he likes talking to this other woman. It could be a friend thing for him but more for her, it's always dangerous to accept your man being friend with anyone that calls them sweety and texts all the time it could be understandable maybe once a day or once every few days but not everyday, that is going too far and if your boyfriend cannot make changes to make you happy then you have to question how close he is to this other female. He could limit the text to once a day or once every few and explain to this girl that you have a problem with the constant texting. Though it is possible for a man and woman to only be friends there are boundaries that relationship cannot cross and she seems to be crossing those boundaries constantly. What I would do is meet her and show her that you are a happy couple so that she see that you are not going anywhere but it's up to your boyfriend to limit the contact that he has with this woman maybe suggest that to him saying something like, "I don't mind you talking to her it's the amount of times that you do talk to her that bothers me" or "Could you compromise and only talk to her once a day and not all day everyday" if he sees that you are willing to compromise with him it will not only make him want to please you but also appreciate that you aren't trying to control who he talks to.
No you are not wrong to think that he can not be committed enough to you if he has another female interfering in your relationship. You cannot help who you fall in love with no matter their race, religion, social status, your parents are going to have to realize that you love this man but also understand that you parents only want the best for you and are afraid to let go and allow you to live and learn so be patient with them. As far as your boyfriend is concerned if there are people in the way of your happiness then you have to push them out of the way maybe he should not answer her text for a while and see if that makes things better. What you are going to have to do is explain to your friend that your boyfriend has an issue with him and in order to make your relationship work, there comes a time when we have to grow up and find our own happiness and relationships are tough enough without adding other people to the equation.
You need to explain to him that you will not accept his proposal until this issue is dealt with and if it doesn't change soon then your relationship is in big trouble. If he see the seriousness of the problem then maybe he will be more willing to make that decision of whether to tell the friend she is overstepping boundaries and to respect your relationship or maybe you need to walk away from the relationship but make walking away your very last resort because you don't want to live with regrets of possibly letting a good one get away over an issue that can be solved through communication and trust and some type of respect from both ends. What you both need to work on first is being able to trust each other before you take such a big step as engagement. Maybe compromise if you stop contacting your friend maybe he will do the same so that you can concentrate on your relationship and each other but if you put condition on your relationship it will only show that you do not trust each other.
He should expect you to be friend with someone that you feel is threatening your relationship with him he is living in a fantasy world and as far as your best friend is concerned I was just giving you some suggestions as to how to fix the relationship and that was one possibility. You are not wrong to think it's absolutely crazy to think that you and this woman that constantly disrespects your relationship could ever be friends. He has some kind of emotional attachment to this woman but he also feels that your best friend has feelings for you and is in a way disrespect him and this is something the two of you are going to have to work through before not only considering marrying him but considering staying in the relationship if you can not work something as simple as another female threatening your relationship then your relationship is in deeper trouble than you thought. I would still suggest ask him to compromise and lower the times that he talks with her during the day as a start and then you could continue to compromise to the point where he doesn't even talk to her on a regular basis. You aren't so much being a hypocrite whereas you aren't considering his feelings about the best friend just as he is not considering yours and you have to sit down and talk this out.
Maybe have a heart to heart with your best friend telling him how your boyfriend feels about him but like you said you don't want your friends and family to think badly of your boyfriend and really this should stay between the two of you. There has to be something the friend does that makes your boyfriend feel he wants you for more than a friend and your boyfriend could be thinking the same thing that you haven't cheated physically but that you may have too much of an emotional attachment to the best friends. You both need to learn to trust each other and allow each other of have friends, are you sure he doesn't address everyone as Sweetie? I would met her just to show her that you are in the picture and in it to stay, If she see for herself maybe she will back off on her own without anyone having to talk to her.