No, they cannot
Not at the same time. Additional information: The Vice-President serves as President of the Senate, but is not a Senator. He can only vote in the event of a tie.
The time is not specified. This could be any event, any time.
No, they have to be of the same political party.
No.
Mardi Gras
Next in line after the VP is the Speaker of the House.
The story takes place during the Great Depression, so the President at the time was either Herbert Hoover or Franklin Roosevelt.
The Senate
If they were all died at the same time, or almost the same time, the president pro tempore of the US Senate would be sworn in as President. Under reasonable circumstances, there is a procedure for replacing all these officials in a fairly short time.
If the vice-president and the speaker of the house were to die at the same time, the President pro tempore of the US Senate would become president.
The purpose of the 25th amendment to the US Constitution is to establish a line of succession from the President. This amendment determines who should become President in the event that the President is no longer able to preform his duties.
C S Lewis died on the same day that US President John F Kennedy was assassinated.