They recommend 80°C / 175°F: https://aeropress.com/use-it-now/getting-started/#steps

I believe the water should be just below boiling. I tested it with a thermometer and it seems to settle at the right temperature in a few seconds after boiling, if I open the electric kettle and let it vent.

Almost boiling, up to the point where the kettle really starts to make noise and bubbles are forming.

I just eyeball it honestly. You'll know when you poured the water too hot from the bitter taste :)

I think it depends on beans (dark roast is fine with lower temperatures), but I go with ~99ºC water.