"I did everything in the item above, got the content initialization message, but the quest still doesn�t start."
You may need to go into the hallway connecting Vault 101�s front door to the outside world, then go back out. Then wait a few minutes and you�ll get a notice about a radio message; use the newly revealed radio signal to find the quest.
"Was I supposed to be able to go so far outside the simulation map�s normal geometry?"
Supposed to? I don�t think so. Able to? Yes, in at least two places. I don�t recommend doing this, because it means you�ll miss out on a few sub-quests (and their associated experience points and Gamerscore benefits). That said, there may be benefits in doing this for speedrunning purposes.
"I�ve finished the simulation, but can�t replay it."
Bethesda really ought to see about fixing this with a patch. But in the meantime, make a save file just before you get into the sim pod. This way, you can reload the save and replay it from there. You may not be able to replay it any other way at this time.