Why did Byakuya get fat?

It appears they found comfort in fast food which was always similar regardless of location. They became very enthusiastic about food and decided to gain a heavier build.

Is Byakuya Togami alive?

Byakuya further added that, as long as he were alive, the Togami Family would never truly die; Byakuya Togami is still alive, and he vowed to rebuild his family no matter what opposed him once he entered the outside world.