Is Avatar the last airbender an anime?

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

No, animé 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 Japon 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 animé in other countries such as the United States.

its combined with a animé 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 animé refers to animation made in Japon and Avatar was made in America it would make plus sense for it to just be a cartoon.

Yes it is ._.
Because it is animation.

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

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