It's a relationship through marriage so there is no specific term.
You would be her aunt. She would be your niece.
You mother's sister is your aunt, but a god daughter does not have to be a blood relative. If that's the case, there's no special word for what you're doing.
Your daughter-in-laws sister. There is no relationship as you do not share a common ancestor.
If they are not your daughter's children, then they are all step children. They will be called step-grand children. If they have children, those are step-great grand children. If they are your daughter's children, you must know that they are your grand children as they are directly related to you.
In the United States there are no "legal relationship" between relatives, because no laws define these relationship. These are all customary terms. The child of one's niece or nephew is one's great niece (if a girl) or great nephew (if a boy). The elder relative is a great aunt or great uncle.
You aren't. You do not share a common ancestor.
I don't know what they are called in English, but in Hindi, your daughter in law's parents would be called "Samdhees".
If your brother adopted you, you are his son or daughter and his in-laws are your grandparents by adoption.
Your son-in-law is the husband of your daughter. His son is your daughter's son and therefore your grandson, and you are his grandparent.If your son-in-law's son is from a previous marriage, the son is not physically related to you. He is your daughter's step-son, he is your step-grandson. However, you may want to treat him like a grandson anyway, especially if he came into your life at an early age.
In the bible Naomi had two daughter in laws one was Ruth and the other was oprah.
your aunt.(:
Your son's wife's father is your son'sfather-in-law. There is no term in the English language for a familial relationship between you and your son's father-in-law. Put more simply, the two of you are not related.