The mother can apply to the probate court to be the executor. In this case the parents are entitled to the estate. There is probably little to distribute and nothing in the way of legal property. You might consult with a probate attorney to see if it is worth hiring them to assist, but they will probably say it isn't worth it.
Marriage does not affect the rights to inherit in the US.
No. Adoption removes the rights to the biological parents' estate.
You should seek the advice of a real estate/estate planning attorney in your area who is familiar with the property laws in your state. There may be tax consequences. You should also discuss the consequences of a conveyance to your married daughter under the statutory provisions of your state.
Your brother's estate would be distributed according to the laws of intestacy in his state. Generally, his parents would be his next of kin. If his parents are not living then his siblings would be next in line. You can check the laws in his state at the related question link provided below.
You need to step up and make claim against his estate as a possible heir as soon as possible. Contact an attorney about this. Biological children have inheritance rights even if their parents were never married.
No. What you inherit is yours, not his, and it isn't community property.
The executor has no control over how the estate is divided. Each state has laws on how the property is divided when there is no will.
It is not the parents, but the estate that is responsible for any remaining debts. That will include medical bills. If there is not enough in the estate to cover them, someone will not get paid.
I am assuming that your grandmother does not have a spouse who is still living. In California, if a resident dies without a will or trust, then the laws of intestate succession are used to determine who will inherit the estate. If your grandmother was not married, then the estate would be divided in equal shares (if they are in the same generation) to her children. If there are no children or grandchildren living, then the estate would go to her parents. If her parents are no longer living, then the estate is distributed to the "issue of the parents." (Issue is the legal term for children, grandchildren, etc.) I am not an attorney but typically, in your situation, you would inherit one third of the estate. (Your father's portion.)
The estate.
An estate agent is an agent who is in control or charge or the estate. The auctioneer is the one who is going to get the most money they can from the estate and property.
Generally, if the decedent was not married and had no children the parents are the legal heirs in an intestate estate. You can check the laws of intestacy in your state at the related question link provided below.