I hate the idea of using less than a size 6.
In my mind the carp, if it decides to take your bait into it's mouth, will do so regardless of size hook (this is presuming you alter the bouyancy of bait and hook together to at least that of the average freebies you have fed).
Once in the mouth, what has more chance of catching hold? A size 10, or a big old sticky sharp size 2?!
Hence the smallest for boilie fishing i'll ever use is a 6, i'll only go smaller for freelining, zigging or floater fishing.
On hair length, on very clean gravel with a big snowman (18mm bottom bait or bigger) and a size 2 I use 10-20 mm gap between bend of hook and bait. Smallest I use is a 5mm gap, popups included.