The cemetery's operator, which may be a municipality, county, religious body, private company or volunteer group. Closed cemeteries' records may sit with local government or historical societies.
Yes. Funeral home files are private business records, so access depends on the business's policy and applicable law.
No. Burial usually follows days later; the date of death should come from the death certificate or medical examiner records.
Usually not. Many are volunteer indexes, which are useful leads but should be confirmed against the cemetery's own records.
Both often rely on information supplied by a relative under stress, so spellings and dates can vary and should be compared carefully.