Why was aang sent to the eastern air temple when he was a male airbender? Was there some sort of exception for the avatar? Maybe there is some sort of exchange program? I'm kinda new to this fandom, so I don't really know much yet.
Well, there was indeed an exception because he was the Avatar.
As seen during the Storm, the Monks of the leading Council of the Southern Air Temple feared that a war would break out soon. Since they felt Aang was not trained appropriately for his role as the Avatar by Gyatso, he was send away to the Eastern Air Temple. The point was to separate Aang from Gyatso, so by sending him to the Easter Air Temple, it was impossible for Gyatso to "follow" Aang (in contrast with if he would have been send to the Northern Air Temple, or if someone else at Southern Air Temple would have become Aang's tutor).
The monks knew the fire nation was plotting an attack, which is why they revealed the Avatar early, so that he could train early and protect them. They saw Gyatso as too lax and not sufficiently preparing him, so they wanted to separate them. They chose the eastern temple in particular because it's the furthest away from the fire nation.