Pepsy left a document related to "The Great Fire of London." Did Pepsy make his own stenography? Or did he use one of the stenographys at that time when he keeps a diary?

Pepys (note the correct spelling) wrote in longhand. There were scribes who could copy for a fee, but everything was written in longhand at that time. There were no typewriters or computers.

For publication, a printer would set words in type, but that could not be done at home.