Is Avatar the last airbender an anime?

No.
Avatar is my new kegemaran Melodic Death Metal band.

No, Anime is made in Japan, I believe Avatar was made in America

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

its combined with a Anime 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 Anime refers to animasi made in Jepun and Avatar was made in America it would make lebih sense for it to just be a cartoon.

Yes it is ._.
Because it is animation.

Anime means Japanese animasi so no it most certainly is not an anime.

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