Was Sids unhappy that Dooku

cut off the arm of the choosen one.. thus kinda crippling him? Also, did dooku know that Yoda could stop that huge pillar from falling on the duo... Seems like Sids would've been really unhappy had Dooku killed his choosen next apprentice.. yet Dooku still cut off his arm and tried to kill him.

In RoTs.. was Dooku's instructions to kill Anakin and Kenobi or was he simply testing Anakin and had no intention of killing him?

He might have been unhappy, sure, but I've been of the opinion that while Sideous had a lot of plans for Anakin, he wasn't 100% necessary for his plans of galactic domination. Palpatine's a smart man, and I think he knew better than anyone that with the type of lifestyle Anakin had (being a Jedi), he could die at any moment, any number of times, and there isn't really anything Palpatine could do to prevent that.

So if Anakin ended up getting butt****ed by Dooku and died, well, "that sucks". But the plan would continue.

I mean, when you think about it, Anakin never even really played a pivotal part in the Empire. Even without Anakin, the 501st could have sacked the Jedi Temple. Even without Anakin, Palpatine still had the emergency war powers to control the military. Even without Anakin, he still had the massive power of the Empire to control the galaxy.

TL;DR: Post-PT Vader, and Sideous' reaction to Vader being what he is (a shell of his former self) answers your question pretty well.

I'm pretty sure Sidious would have told Dooku to test Anakin.
And an arm hardly dimishes his already insane potential.

Nah. Not like the HAND made much of a difference, anyways.

I think he was probably pleased. It would have a very minor effect on his overall power (if any) and would embitter him and fill him with resentment, which is valuable for turning him. Palpatine even used it in ep 3, trying to make Anakin accepting of his desire for revenge.

Had it been both arms or something hed probably have been kind of annoyed, but at the same time he lives by the sith rule of survival of the fittest and might have concluded Anakin was just too sentimental and weakend by his Jedi mentality to be of any use anyway. Like Tzeentch said, the plan would move on regardless so its not a catastrophic loss to him by any means.