When Salamanders and Razordons go in front in close combat does the entirety of their crew make up the second rank. Or do only two skinks per Salamander/Razordon make up the second rank with additional handlers forming a third (and theoretically subsequent) ranks. On one hands ranks for everything else are equal and the BRB doesn't say monsters and handlers are different. On the other hand the BRB says the handlers can attack things in base contact with their monsters. It doesn't say the handlers in the second rank can attack things in base to base contact with the monster. Either way a small number of skink attacks is unlikely to matter in the grand scheme of most battles.
The basic rule book says that the handlers arent a combat unit and are ignored for most purposes and the monster is the extent of the unit. It also says later that handlers cannot be charged attacked or affected seperately from their monster. You just move them out of the way if they are blocking movement or line of sight. Basically they dont count towards ranks. Just set them up however you would like. They get to attack anything in contact with their monster. The handlers are essentially a 5+ ward save for the monster, since for every wound the monster takes the handler takes the wound on a 5+.
Cyanhawk is correct. You won't end up with any ranks since you can only have a unit of 3 anyways and the handlers don't really have to be on the board so long as you know how many are left alive. They just get to attack what the monster can attack.
On a slightly related note I had an interesting situation come up in a game the other day. My unit of salamanders was garrisoning a building in the center of the board. They got charged and we went into a building assault. Now usually both sides bring 10 models into the fight for the building. My contention was that my two sallies counted as 6 models (each being 3 models worth due to being war beasts) while my 7 handlers didn't count for anything (as said earlier, they are just kind of there). My opponent believed that they would count for my 10 model limit and thus could only bring 4 to the fight. What is the correct interpretation for this in case it happens again?
No the opponent would be wrong treat the monster/handlers as one unit with 3 wounds. The handlers are free attacks on the salamanders profile. And really they are only s3 attacks at ws2 so your opponent shouldn't be too worried about it.