Something I seem to be missing in rulebooks or official FAQs...

In our last game, we were four players/Investigators going against Cthulhu. Near the completion of the third Mystery, the AO awakens. The game goes on, we solve the third Mystery and then Cthulhu appears at space 3. His token says he has "number os Investigators+3" life points - so, at that moment, 7. Before any of us could get to it, three Investigators are devoured, and out of game as well.

What happens to Cthulhu's life points? They remain 7, because it was the number of Investigators alive when he was put on the board, or they become 4, since now there is only one Investigator?

Either way we won - the remaining player was an "Ancient Ones Killing Machine" anyway -, but the doubt remained in the air

The investigator silhouette icon gets its value when the game starts, so in your case it would always be 4 (and thus Cthulhu's toughness will always be 7 in your game).

Even if the number of investigators changes after the game starts, the value of this icon is constant.