LeCig makes the PigCig big batts. I have the 1300mAh/3.7v kit, it's KR808D-1 and lasts really long. They also sell an 808/510 adapter so I can use anything out there on them. That being said, I still have a lot of 808 stuff I'm using but don't think I'd buy another 808 device once they're used up. Most everything is 510.
A1: You'll most likely need a new charger for any big batt no matter what you choose, the other stuff/devices can be reused with adapters (they only cost a couple$ ea - 808/510, 808/eGo, etc)
A2: Yes, big batts last a long time. I was going through a couple of my 808 little batts/day, 1 PigCig lasts more than a day
A3: Depends on what you're looking for here. If it's more juice, there are mega carts that will hold a couple ml of juice (the little carts usually hold 1). If difference in temperature or throat hit, you need to look at different resistance cartomizers. There's tons of threads on this subject, bottom line LR cartos (~2.0 ohm) = warmer vapor, SR cartos (~3.0 ohm) = cooler vapor. I still use the "Premium Coolcarts" blanks for my wife on the little batts (she likes cooler vapor) but there are cheaper ones out there.
P.S. I wouldn't use anything under 2.2 ohm on a small batt (anything less than 450mAh), really LR draws too much to be safe on them.