no
yes
Biological children can be eligible for survivor benefits when are of minor age and a parent dies. The termination or relinquishment of parental rights does not always relieve the requesting parent of financial obligations to his or her children, unless those children have been legally adopted. Whether or not a minor child qualifies for SS or SSI benefits would depend upon the individual's circumstances.
No
Inheritance.
Morally and ethically yes, but not legally.
Yes, and very often to extremes.
If there is no will, the law normally splits the estate between the spouse and the natural children.
If your parent dies and there is no will, there is a legal order of inheritance. The surviving spouse is next in line, then the children.
They can be sued.
Social Security Death Benefits until age 18.
To be sure I understand your question, let's say, for example, you have custody of your child, and you want to know if you die can you keep your ex from receiving Social Security suvivor benefits. Do I understand it right? If so, then NO, you cannot prevent the child's other parent from receiving SS benefits. If you have custody, I assume the other parent is paying child support. If not, you need to taket him or her to court and sue for it. If s/he is paying child support, then that's good. If you are concerend that if you die the other parent would squander the money at the expense of your child (neglect, etc.) then you need to talk to an attorney to see what can be done. But this will be a tough one since it is customary for the surviving parent to receive SS benefits for the minor child if the custodial parent dies.
If a dependent parent dies then the estate will be responsible for their tax debt. If you are over their estate then you would have to ensure that the government gets their taxes.