Thrall appoints Garrosh as acting warchief. How much ever you oppose this decision of making Garrosh acting warchief, when Thrall suggested to be his advisor the most rational (I believe it's perfectly rational) thing to do would be to accept it.

Even if it absolutely seems like horde orcs (not cultist orcs) are behind those attacks, there does not seem like a direct link to Garrosh. Even if it were the case that Garrosh's personal bodyguards attacked elves and hamuul, when he denies those allegations you try to dig deep. Let him atleast provide his side of defense. Deciding that he is guilty based on situational evidence is rash.

Garrosh has always been a hothead, there was no doubt that he would accept the challenge. Cairne is, although, a seasoned leader. He should know better. Would it have been so hard to decline Garrosh's challenge of "duel to death" providing a reason like "I do not wish to kill you, just defeat you and claim the throne for the sake of our people." That wouldn't mean he was gonna come out of the duel alive (what with poisoned gorehowl and all) but accepting such a challenge is insane. Whoever wins in "duel to death", horde would lose one leader.

And the most important bit that made me wonder if Cairne was in his right mind: he hadn't appointed any second in command, or atleast didn't inform him about what he was gonna do. Even if you are absolutely sure you are gonna win, you always appoint a second in command. All those taurens wouldn't have died if his second in command knew about this duel and took measures to sieze control as soon as Cairne died. Leadership is more than just about right or wrong, it's about responsibility.