Is Avatar: the Last Airbender an anime?
Anime basically translates to animation, so the Japanese don't really have a distinction. Claymation for example could qualify as 'anime' in the East.



From a Western perspective, 'anime' is a looser term, generally meaning animations from Japan, but sometimes it's applied to Western shows with the anime 'look', like RWBY or Avatar.

There's no strict guideline on what qualifies as anime and what doesn't, and arguments arise frequently online by people with different opinions on this. 

It's safest to say Avatar is anime-styled.

In regards to the 'manga' of Avatar, it seems to be commonly referred to as a comic rather than a manga. But the format of this should have no bearing on the animated production.