Are Kirito and Asuna still together?

And Kirito lives for Asuna, in the SAO arc remember how he poured his heart out to Asuna, saying that she is everything to him, that he lives for Asuna, and that they both will protect one another.

Are Kirito and Asuna engaged?

Kirito reveals he feels the same and gains the idea for them to leave for the 22nd floor and buy a house together and boldly, Kirito proposes marriage to Asuna, who tearfully accepts.

Do Kazuto and Asuna break up?

No, they never did break up in SAO, sorry. They are together forever!

Does Alice Love Kirito?

Yes Alice does in fact love Kirito. At the end of this cour in the anime, Kirito will be in a coma for 5 months and Alice will take care of him. She will gradually start to fall for him over that period due to the events were seeing played out between them outside the tower and whats to come.

Is Kirito dead?

Because Kirito lost after that, technically they are both dead. However, Kirito won after that, and Kayaba agreed to make sure Asuna didn't kill herself, but she did. The only resolution therefore was to keep her alive. As for Kirito, it seems to be that Kayaba wanted him alive to talk.