First, any Avatar can go into the Avatar state. Only a fully realized Avatar can control it. Otherwise, it's a defense mechanism.
He regularly got pushed into the defensive Avatar State. During the escape from Ba Sing Se, Aang realizes what Guru Pathik was teaching him, let's go of his earthly attachments (Katara, much like Zaheer did when P'Li died), ...
Depends on how you measure being a prodigy
There are four Avatars that viewers have seen learn the four elements: Wan, Roku, Aang, and Korra. Unfortunately, this gives us a small sample size.
Wan was the first Avatar and didn't become so until later in life. Given that he's the only one who wasn't the Avatar from birth, I don't think it's really fair to ...
As explained here Can the Avatar still be reincarnated?
Actual Avatar reincarnation means Raava accepts part of current Avatar soul, leaves its body, and finds new Avatar. Communication with previous Avatar incarnations was exactly communication with parts of their souls inside Raava. Since Raava got itself destroyed, and then resurrected, it is in "...
Honestly, I got the same doubts when I watched this season yesterday. However, I am going to try answering your questions. Please keep in mind that I didn't watch previous three seasons, so I might lack some knowledge about this bending world, so correct me if I am wrong somewhere.
Are all these events possible?
Apparently, they are.
Is it truly Amon'...
In LOK, Toph Beifong is shown as big chief of police
The chief of police in (present time) Legend of Korra is Lin Beifong, Toph's daughter.
The old lady you see is Toph Beifong, Lin's mother and the earth-bending blind companion of Aang in Avatar The Last Airbender.
Notice that Toph retains her original hairstyle from ATLA.
Toph is ...