Signing on behalf of someone

Q: Is it permissible to sign something in someone else's name if they give you permission?

For example, my younger sister needs my parents to sign something for school and my parents are not in the city. If my mother gives me the permission to sign the paper in her name because she is unable to, is this permissible?

Marital problems

Q: I am separated from my husband through khula as we both were facing issues in our marriage. I wanted to stay with him but his parents did our istikhaara and said it's not good for us to continue together due to which we had to separate. By any chance, is there any wazifa through which we can reconcile? We are not on talking terms with each other.

Wine vinegar

Q: I would like to ask you about the Brandywine vinegar as I am studying in Germany and almost every other has this Branntweinessig and they use it as a cheap preservative for yogurt, ketchup, mayonnaise, even some milk drinks also have this. So is it permissible to use this or not as due to language barriers I could only rely on translation which literally means wine vinegar.