I'm semi-old school, so I can answer some of these questions, but not others.
1.) 2nd Edition is AD&D, but there was also a version of 1st Edition that was also AD&D. There was a basic version and an advanced version. When 2nd Edition came out, there was only the advanced version. When 3E was released, they were like, "why call it advanced if there's only one version?" so they dropped the 'A'.
2.) From my understanding, no. OD&D was before 1E. The corebooks for both 1E and 2E were the PHB, DMG and MM. I'm not sure about OD&D, though.
3.) I'm pretty sure that was OD&D.
4.) Actually, they're very, very similar. Especially if you strip 2E down to core only and don't use any of the optional rules. On the other hand, if you utilize all of 2E, including the Player's Option books, then they become much more significantly different.
5.) I can only really speak for 2nd Edition, as my experience in the older versions are very limited. But old school games do have a different feel from the newer ones. Lethality is higher, there's far less customization and character building, the rules are much simpler and there's far more DM fiat. It only takes about five minutes to roll up a character and there's little to keep track of, especially if you are not a caster.
Also, the word 'balance' has a completely different meaning in the older games. In newer games, balance means every class is equal. In the older games, it meant that things would eventually balance out over time. For instance, fighters start out really strong and mages are pathetically weak. But after you gain enough levels, then the mages become much stronger while the fighters fall far behind. Different classes have different XP tables (thieves level up faster than fighters, who level up faster than mages). And magical items are cool things that make things easier, but are in no way required to survive.