Most likely the initial firing of the Halos. It is strongly implied that he had a conversation with one of the last humans Forerunner who was tasked with pulling the trigger on the gun pointed at the head of the universe.

5 year-old explanation: Light bulb was talking to scared puller-of-lever from Halo's first firing.

: 2. Why did Regret jump the gun and send his ships to Earth before the rest of
: the Covenant.

As Cortana pointed out, humanity's presence on Earth was unexpected, so there was really no reason for Regret to hesitate a jump with his escort. This can explain the unorthodox use of funny-shaped bombs (likely used for excavation) to get past humanity's defenses.

5 year-old explanation: Hairless llama man didn't think people would be on Earth.

: 3. What did Truth dig up in the Legendary ending of ODST?

The Dreadnaught's "keyhole" / massive Ark portal

5 year-old explanation: Plot device.

: 4. What questions did the Gravemind ask Cortana, and what answers did she
: give?

"Tell me about yourself" "What are you studying?" "How 'bout them Redskins?"

5 year-old explanation: "Why you nakey?"

: 5. If blowing up Halo is enough to stop the flood from spreading, why did the
: Forerunner not just blow up all the Halos? Yay, flood gone!

Blowing up Halo would only stop the local infestation, as containment of the specimens saved for study on that specific ring was breached by the covies.

5 year-old explanation: Local flood only.

: 6. Why does the Covenant hate humanity again?

Because 343 have no real skill in developing a franchise anew. This would be understandable if they hadn't snubbed an established writer (Nylund) in favor of a mediocre feminist and a collection of weak amateurs that make Joe Staten look like Jules Verne.

5 year-old explanation: Because 343 and want to make big money with as few expenses as possible.

: Many thanks.