Is avatar the last airbender an anime?

No.
Avatar is my new favorite 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 Japan it is not considered an anime. But in Japan, "anime" refers to any form of animation 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 animation made in Japan and Avatar was made in America it would make more sense for it to just be a cartoon.

Yes it is ._.
Because it is animation.

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

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