Different people different answers!
1) From Hook to Boilie, between 5-10mm.
2) Rig length, the majority of Carp Anglers todat are using rigs between 6-12inches long, so be different from everyone else if you can. The rig length can be as long as you want it, depending on your situation. Bear in mind though that Shorter Rigs CAN/MAY lead to increased Hookpulls. (See Complicated Rigs Thread).
3) The hair loop I just tie an Overhand knot at the end of the Hair before I tie the Hook on if I'm using Bottom Baits.
4) I use Kryston Merlin for much of my fishing, although after some comments on here I will be trying to get on with SuperNova. Other Braids I use are SuperSilk, Silkworm and Deception.