Is অবতার the last airbender an anime?

No.
অবতার is my new পছন্দ Melodic Death Metal band.

No, জীবন্ত is made in Japan, I believe অবতার was made in America

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

its combined with a জীবন্ত 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 জীবন্ত refers to অ্যানিমেশন made in জাপান and অবতার was made in America it would make আরো sense for it to just be a cartoon.

Yes it is ._.
Because it is animation.

জীবন্ত means Japanese অ্যানিমেশন so no it most certainly is not an anime.

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