A few answers
1. Is the game always dealt face down in a casino?
Nearly always. There are a very few exceptions to the rule, but they are rare.
2. Are most of these games 6:5 or 3:2?
For now, most double-deckers are 3:2, with a few exceptions in Las Vegas, but, as noted above, these are rare.
3. What are the most common double down and split rules?
Double on any 2 cards. Split up to 4 hands. No re-split of aces. Still not uncommon is double after splits, but it's getting less common all the time.
4. What other major changes does the game have versus shoe games?
Far more double-deckers are H17 as compared to shoe games. Surrender is rare in double-deckers and more common in shoe games. Penetration tends to be worse in double-deckers, although there are plenty of poorly penetrated shoe games as well. The cut-card effect is more pronounced in double-deckers, where it is not unusual to find cut-cards, as opposed to shoe games, where the cut-card effect is minimal. Double-deckers are slower than most shoe games. Many double-deckers have no mid-shoe entry rules, which are less common in shoe games. Preferential shuffling is often seen in double-deck games, especially on the Strip. Casinos tend to hawk double-deck games more than shoe games, and a few double-deckers are counter traps, especially the ones with good rules.