Are there any Quranic or Prophetic texts indicating man's awareness of what is happening around him from the moment of death until burial? And what are the details of what the deceased experiences in his grave, such as hearing, seeing, and being questioned by angels? And does this differ for the martyr?

The gist of the statement is generally correct. What was narrated from the Prophet, peace and blessings be upon him, was not the command to sit for an hour after burial; rather, it was narrated from Amr ibn al-Aas. The hadith "The torment of my Ummah is in the graves" has not been narrated. Rather, the Prophet, peace and blessings be upon him, said: "Indeed, this Ummah will be tested in its graves. Were it not that you would stop burying each other, I would have supplicated to Allah to let you hear the torment of the grave that I hear." And it has been authentically narrated that the Prophet, peace and blessings be upon him, said: "The torment of my Ummah is in its worldly life."