Since this is the adoption category I assume you mean not the biological grandchildren but foster kids who have never been adopted. And no, they have no right at all to anything their foster family leaves behind unless they are mentioned in the will.
If you mean biological children they inherit their parents who in their turn inherit their parents, your grandparents. So unless the grandchild is mentioned in the will or the parents are deceased, the grandchild will not inherit the grandparents.
A proven biological child is usually entitled to a portion of her father's estate.
No. Adoption removes the rights to the biological parents' estate.
If you live in the US (and without knowing the state) generally speaking, adoptive or biological is irrelevant. If there's a will and the child is not named, the child gets nothing, unless they can successfully contest the legality of the will (which takes a strong case).
no
In most places, adopted children have the same legal rights to inheritance as biological children. This means they are entitled to inherit from their adoptive parents' estates just like biological children are. Adoption is a legally recognized process that grants the adopted child the same legal status and rights as a biological child in the eyes of the law.
Only if you adopted the child.
If he legally adopted you, perhaps you might be an heir if his estate is intestate. You should speak with an attorney in your jurisdiction who is familiar wth your state probate laws.
The adopted child have the same right as the biological child.
In the United States a minor child is entitled to a portion of a deceased parent's estate. In some states an adult child is entitled to a statutory portion of the estate of a parent who died intestate. Any child who is next-of-kin to someone other than their parent would be entitled to a share of an intestate estate. You would need to be more specific and check your state laws.
Hitler had no children, biological or adopted ones.
A birthfather is the biological father of an adopted child, or a person's biological father.
No.