Hi
Most hospital records deposited at local archives for safe-keeping are usually closed for 100 years after the last entry in whatever the document is.
Before 100 years, you can usually make an application for a transcription of the records on production of the relevant death certificate.
As to the burial, you should check the cemeteries and graveyards close to where the family was living. Failing that you'll need to extend the search to a wider area which includes the hospital.
Dawn