I am sorry for the delay, but I was on sick-leave and could not address the questions timely.
I did some research on your situation and found out the following:
1. You will not have to drop your asylum claim in order to leave the center and to live with your partner. You will have to go with your fiance to the office in charge for your finanacial support and apply for leaving the registration center and live with your partner. Usually you will need the consent of the landlord of your partner and there have to be a "Untermietervertrag" in order to get the permission.
However, this is only possible if the move is within the town where you are obliged to live(Wonsitzauflage), this is stated in your Ausweis.
2. In regards for the upcoming interview- I would suggest to consult with your lawyer, but my suggstion would be not to skip the interview but mention in the interview your personal situation and that you are in the process of getting married to a german partner.
But as I do not know the details of your asylum claim, it is important to consult the lawyer,
I hope I could help you, if you need further clearification please do not hesitate to use the community.