The Didact did not die at the end of Halo 4. The Didact did not die during the events of Halo: Escalation. Contrary to the impression many have, he is, in fact, still out there…

What happened to the UR-Didact?

The Ur-Didact was eventually exiled on Requiem, not to be awakened until 2557, while the Bornstellar-Didact served during the final days of the Flood conflict, and was also the individual responsible for activating the Halo Array.

Why is the Didact so tall?

Like a couple meters at least. The Didact is so dang tall because he's Forerunner. I'm pretty sure he even ran into an old Warrior-Servant at one point during Greg Bear's Forerunner Trilogy that was bigger than him. Warrior-Servants are bigger than most Forerunners anyway because that's the nature of their Rate.