Yes he is in anime.
He survives, and so does Kurome and Mine. Tatsumi and Mine get married and retire from the Night Raid and have a child together, however Tatsumi remains as a dragon.
Kurome and Wave also go and live off together.
To be honest, I like the manga ending more than I do the anime. It is the ending where he survives and then he marries Mine. A much happier ending than in the anime, where he dies straight-out.
No he died in the anime. Just like Wave said. He and Esdeath now spend time together with each other in the heaven.
What do you think?