Who ever said you had to grow up in this society? It does necessitate that one had to exist, but nothing about you growing up there.
You don't need a large criminal underworld to have Thieves' Cant. What you need, is a large number of criminals, who have reason to want to talk to each other without anyone else noticing. I find it had to believe that there are that many settings that wouldn't fit this requirement.
Yes, which could happen in any number of ways. A gentlemanly thief doesn't just jump out of bed one day and steal the crown jewels. He needs to spend a long time learning how to open locks, sneak around, disarm traps, bluff guards, and fight dirty. Where do you think he learned all of this, a book?
This I don't think should be true. It should be possible for other characters to learn Thieves' Cant just like any other language, but we don't have all of the rules for that. It would also make sense to spread out the Thieves' Cant a bit more.
I don't have any problem with giving the thieves' cant to a background, I simply don't see why it can't be on the rogue, as well.
This is actually another problem that I hadn't brought up yet. The fighter has even worse issues with this than the rogue. I'd actually far prefer to see the fighter be narrowed in scope a lot, because currently, the fighter seems to make just about every other martial character obsolete. If it were up to me, a fighter would be required to have learned a "school" of combat. Where and how he learned that school would still be up for debate, but it would make the fighter more of the wizard of martial classes. They learn by study and rigorous practice.
This would make other classes, like the Barbarian and the Monk much more able to grab a part of the martial pie, as it were, instead of forcing them to become another kind of spellcaster, as they were in 4E.