My father died without a will. Can his children just come into his home and take what they want?
No. No one has the legal right to take any of your father's personal property. His property - his things - belong to his probate estate. If the estate is large enough to require probate, then only the executor or the administrator of the estate has the legal authority to take control over your father's personal property. If anyone takes it, then the executor can sue the person who took it to make them return the property and, in some circumstances, force them to pay twice the value of the property taken from the probate estate.