It depends. If the cabbage wants to dive into it, it probably needs to be at least two cabbages deep. If the cabbage just wants to do the backstroke, a half cabbage depth would suffice.
Probably a 1/2 of a cup every day, or everyother day depending on the soil. You can also water the plant when the soil isn't moist anymore, but you have to pay clost attention because if the soil...