I was watching West Wing today, and saw the episode where the President invoked the 25th amendment and recused himself from his duties pending his kidnapped daughter being found and returned safely. John Goodman played the Speaker of the House, who was made acting president while the president vacated his office to the residence.
GW Bush twice recused the presidency to Dick Cheney for a colonoscopy, and Reagan did once for colon surgery. I am curious if someone who served as acting president for a period of time qualifies as a former president?
Do we call them "President" in address after they return to normal duty?
Are they entitled to lifetime benefits under the Former Presidents Act?
Are they entitled to secret service protection for life?
At which point are they entitled to these benefits? Ever? After a number of days?
Do we call them "President" in address after they return to normal duty"?
No. Their position as president was temporary and not their elected position. Without such provisions, the office of the President would have to be shut down when the President was not available to execute their duties, which could have significant effects.
Are they entitled to lifetime benefits under the Former Presidents Act/to Secret Service Protection for life?
No, simply because they mere executed the duties of the president, and was not actually the president.
At which point are they entitled to these benefits? Ever? After a number of days?
They are only entitled to these benefits if the president becomes permanently unable to execute his duties (i.e. dies) or resigns his position. For the Speaker of The House, both the President and Vice President would have to have vacated their offices. As acting president however, Secret Service protection I would imagine would be granted for the duration of their service, if not already granted (VP already enjoys Secret Service protection). It wouldn't do well for the acting president to be assassinated. Otherwise, these people are simply acting as President and are not the president. I'm not sure if its proper to address an acting president as "Mr/Mrs/Madam President" seeing as they are not the president as defined in the constitution, but this is drifting away from the question really.
As I said above the main purpose for these temporary granting of authority to the next in line of succession is to ensure the continuity of government. The Constitution is clear in that all powers and duties transfer to the VP (or other officer designated by Congress if no VP) until such time that the President can again discharge his duties which ensures the continuity of government. In practice, I'd imagine that it would have to be a rather emergent situation for an acting president to take action beyond simply being in place. There's only been those three times the 25th amendment has been invoked and in all three instances the president was incapacitated for a few hours at most. But the authority to do so is spelled out.
The answer to the title question seems to be: Former President is any person who, elected to the office of President of The United States, served in that capacity until such time as leaving office, including due to resignation. In 1974 it was ruled that impeachment conviction that results in the President being removed from office, would disqualify them from receiving these benefits.