Is Аватар the last airbender an anime?

No.
Аватар is my new Избранное Melodic Death Metal band.

No, Аниме is made in Japan, I believe Аватар was made in America

In a way, no. Аватар wasn't made in Japan, so in countries other than Япония it is not considered an anime. But in Japan, "anime" refers to any form of Анимация regardless of nationality. Therefore, in Japan, it is considered an anime. It is not considered an Аниме in other countries such as the United States.

its combined with a Аниме and a cartoon so its a cartoon and a anime.

Not technically. It has an anime-like drawing style. But it wasn't made in Japan.

But kelly1412 has some really cool anime-avatar fanart.

It's sort of a confusing choice between cartoon and anime, since Аниме refers to Анимация made in Япония and Аватар was made in America it would make еще sense for it to just be a cartoon.

Yes it is ._.
Because it is animation.

Аниме means Japanese Анимация so no it most certainly is not an anime.

Well, "anime" is the Japanese word for Мультики and animation, so, in a way, yes, but Аниме really refers to the Japanese made cartoons, so in another way--no.