Is there a fourth part(book4) of the series avatar Aang

No, but they I think should make another. Luckily, there is a series that comes after ALTA which is The Legend of Kora. There are still a few characters from ALTA such as Katara, Zuko, Iroh in the spirit world, and I think Toph but they are really old in it. They also have kids/grand kids of the main characters, which some of them are:
* Three Kids of Aang's and Katara's
* At least five grand children of Aang's and Katara's.
* Zuko's daughter
* Toph's daughter
I hope this answered your question:)

I'm sorry to say, but no, there isn't. But if you want to find out what happens to the gang after the series, there is a book called "The Search" that I found while at Barnes and Noble. It tells the story of the crew finding Zuko's mother. It also tells you about what happened to Azula after Katara beat her.

Unfortunately no. There is no 4th season of ATLA.
But there are actually 3 comics that I know about for the original ATLA series.
1 - ATLA: The lost Adventures.
These are little side stories and adventures of the Aang gang that happened mostly during the original 3 seasons.
2 - ATLA: The Promise.
The events that happen right after the finale of the show about re-building the world.
3 - ATLA: The Search.
Happens after "The Promise" and is about the procurar for Zuko's mother.

Nope, but you can read "The Promise" and "The Search".