1. 1992
Close AM is not an error, it's a variety, and an extremely scarce one at that. It's about a $2000 coin in circulated condition, and about $10k in mint state red, so, yeah, if you were likely to find one every 12,000 pennies they would be a lot cheaper.
2. How many errors and varieties are you looking for? The more you look for, the more slowly you look, but also the more finds you have per X-number of coins searched, so it's a double sword. The key is to determine which errors and varieties are worth the additional time it takes to search for them, and only look actively for those. Almost every date has at least a doubled die variety or two (even if they're minor), so you're very unlikely to get completely skunked if you're looking for enough things.
3. Really dramatic errors and varieties are very rare, which is why they can be worth a lot of money. Don't expect to find a great one in every box.
Edit: Some of the things I've been looking for (also fairly new to hunting): 1992/1992 D
Close AM, 1998-2000 P
Wide AM, 1988 reverse of 89, 1960/60-D small date, 1970-S small date, any doubled dies I consider interesting on variety vista, coppercoins, and wexler's die varieties (all great resources), repunched mintmarks,
Cuds and major die chips or cracks, rotated die errors, clashes, off center strikes, clipped planchets, brockages, broad strikes, multiple strikes in the collar (since out of collar strikes are unlikely to fit in a roll), strike through errors, and a few others