1. The Didact does kinda clear that up during the epilogue, referring to it as 'the mantle of responsibility for all things'.
2. That's not such a huge deal - much like it wasn't when you discovered the Flood imprisoned on the ring in CE.
3. An Elite says it when he emerges from the Cryptum.
3. The fact he says 'The Forerunners have returned' is a big giveaway.
4. Why are the brutes? Why are the Grunts? Why is Lord Hood, in Halo 3?
[quote]What is the mantle?[/quote]
According to the Forerunners, it's guardianship over life in the galaxy - this [i]is[/i] brought up a number of ties in Halo 4, as early as the second mission where you find the gyph in the cathedral that Cortana translates.
[quote]Why was the didact there?[/quote]
He was imprisoned, which the Librarian states in Reclaimer. This is further shown in the Terminals.
[quote]How does cortana know his name?[/quote]
The console at the start of Requiem has a Sangheili broadcasting the name [i]"Didact"[/i] on repeat for 3 years in an attempt to contact him (let me ask you a question: how does she know to call the Gravemind a 'Gravemind' in Halo 2 when he teleports them to High Charity?).
[quote]Is he forerunner?[/quote]
This is a [i]ridiculous[/i] question. When he is awakened he directly states to John that [i]"the Forerunners have returned"[/i] and numerous other pieces of dialogue further make this clear.
[quote]Why is he so fugly?[/quote]
Why is his appearance relevant in the game? It's shown that he botched his mutation in his attempt to gain immunity from Flood infection.