If both parents die without ever written a will stating which of their children obtains what in the things they left behind - property, bank account(s), etc. - do their children have a legal right to those things...are those things divided equally among the siblings or are other judgements determined?
Let's assume, for purposes of explanation, that father dies first and that mother dies at least several months after father. Let's also assume that father and mother had no children who died before they did.
When a person dies without a will, his/her probate estate is divided according to the intestate law of his/her state of residence. Under Florida's intestate law, when a person dies without a will and is survived by a spouse and children who are also the surviving spouse's children, then the surviving spouse inherits the entire estate and the children get nothing.
When a person dies without a will and is survived by children but no surviving spouse, then the estate is divided evenly between the children.
Note that one's probate estate includes all assets that he/she owns, except the following: (1) assets held in an account that has a pay-on-death beneficiary; (2) assets held in joint tenancy with another (or similar ownership form); and (3) assets held in trust.
Also note that, if an estate does not have sufficient liquid assets to pay debts, then assets will have to be liquidated to cover debts.
Finally, I have no idea what you mean by "are other judgements determined."
What if one of the siblings states, while one of the parent is still alive, the he has power of attorney but refuses to show those legal papers to the other siblings, do the other children have a legal right to see those power of attorney legal docs?
No.
The living parent is not aware if such paper where ever drawn up before the first parent passed on.
The authority conferred by a POA terminates upon the death of the principal.