Well sure. The Leviathan's created the AI knowing full well that like all other AIs it could very well turn on them. Because of that they placed limits on it, even it's programming could be considered another limits of sort, so it's not like this is anything new.
Well in this situation it would be new. It wouldn't make sense for them to create an AI that would have limits on how much it's able to control something they never knew about and didn't exist (the Crucible). It would also contradict the fact that their lack of AI limits, brought upon by their hubris, is exactly what caused their downfall and therefore the Reapers.
They never believed the Catalyst could turn on them, that was pretty much the point in the Leviathan DLC.
The Catalyst is clearly following it's coding to find a solution to its problem, but it has very little, if any, limits on how it goes about this. Saying they gave it a small amount of control of the Citadel to somehow "limit" it out of fear that it might rebel isn't supported by evidence. In fact it's directly contradicted by the entirety of the Leviathan DLC.
Well the platforms leading to the Control and Destroy options only rise up after the Catalyst is done talking, was that done by the Catalyst or the Crucible? the timing seems to suggest the former.
The problem with Mass Effect is that consistency isn't exactly a priority for the writers which is the main problem. The rest of the game, especially parts like Tuchunka, Rannoch, and Cerberus have lots of these examples; and then there's all the stuff that happens between games and in the alternate media. Why I'm bring that up is because the story doesn't have the integrity to stand up to close scrutiny and this level of speculation, we know next to nothing about the Crucible for example, and what the game tells us seems highly unlikely and that's before we even start speculating about the elevator.
Crucible by the looks of it. It rises when you're ready to choose, which is when you approach it and/or stop talking to the Catalyst. Seeing as though it reprogrammed the Catalyst to tell you about the options it presents, it's not that big a leap in logic to say it takes a cue from the Catalyst as to when it's done explaining. That wouldn't even need VI level of programming to do, you could program something like that (a cue I mean) with todays technology.
As for your last paragraph, we don't really know if the story has the integrity to stand up to close scrutiny and this level of speculation. Unfortunately fans don't seem interested in speculating. Look at Massively above who claims to either have not considered the Crucible in two years, or who did consider it instead decided to not bring it up because it would cause speculation and might stop people being able to bash Bioware. Look at King Mark or Kel Riever above who don't even try to speculate, instead they just came in and bashed Bioware because lol.
You say it can't stand up to close scrutiny, I say we don't know that because people are far more interested in bashing Bioware due to faulty interpretations of what they saw in front of them. People would rather bash that scrutinise. They would rather hate than speculate (lolrhymes). I love speculating, I love trying to figure out things, but unfortunately too many people on these forums would rather just bash Bioware and hate.