Okay, I'll have a crack at these.
1) Can a pit slave armed with a CLAW special hth weapon hurl opponent, that goes out of action (6) as a result of this round of combat?
As the rules in the rulebook state under injuries on page 17 of the ORB, models that are taken out of action are removed from play immediately. The wording of the Claw Weapon is not ideal, but an additional throw after taking a model out of action would rarely have any additional impact. If you have areas that would inflict instant death, it may be arguable, but otherwise there would be no point throwing the model.
So what about if the model is just taken down, but would, because of combat rules, be taken immediately out of action?
It does create the conflicting issue of events. Does the status of "Down" move to "Out of Action" before the model would be thrown? It does say that the attack is 'in addition' to hitting the opponent, so by that logic it could be arguable that the model would be thrown. However this would mean that the model would be ejected out of combat, which would mean a separate injury roll that wouldn't be affected by regular combat (it would be from falling damage) and would not automatically take the gang member out of action. So if it does happen regardless of the result, then the model would be taken down, thrown and then would potentially suffer another damage roll, but would not go out of action automatically except if the model falls a distance of 12" or greater.
2) Does Pit Slave armed with a CLAW special hth weapon automatically kill opponent that goes down and is thrown with Hurl special rule?
An opponent taken down in combat would usually automatically go out of action (see 1); the only exception is multiple combat (see 3). The only Pit Slave weapon capable of killing an opponent outright in a close combat is the Shears.
The Claw is of most use when an opponent isn't injured but is defeated in combat. In this case the model could be thrown, and then chucked off a ledge and so on. But the rules do not account for instant death even when falling great distances.
3) If answer for above is YES, what happens in multiple combat? For example: pit slave fights two gangers. He wins round of combat against one of them, inflict 'go down' and throw him away. Then he fights another ganger and kills him. Is the 'hurled' victim dead? In normal combat both would be dead, becouse at the end of combat they would be at mercy of their opponent, but hurl separates gangers before that...
It would be nice if you write us down a PROCEDURE for combat and multiple combat with use of a CLAW special weapon and with use of HURL OPPONENT special rule. Actually the 'additional' hits mentioned in CLAW special rules are little tricky.
As I see it, a multiple combat would make no difference to the way the Claw is used. The rules in the ORB state that parts of a multiple combat are fought as if in one-on-one fighting. Essentially if you fought two gangers in combat with a pit slave with a claw, you would fight the first opponent, if you won, you could hurl the opponent. As multiple combats prevent models being taken down and out if there is at least one model from their side still standing, this is a lot easier to justify than a single combat where a model is taken down and out.
Note however, that regardless of the opponent being ejected, the fresh enemy would still get their additional attack dice and +1 bonus to combat resolution. That gang member would then however be taken down and out of action if you somehow managed to win the combat and wound them successfully.