(The HPMOR discussion thread after this one is here.)
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. There haven't been any chapters recently, but it looks like there are a bunch in the pipeline and the old thread is nearing 700 comments. The latest chapter as of 7th March 2012 is Ch. 77.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.
Perhaps Voldemort doesn't want Quirrell to know certain going plans? Perhaps Voldemort thinks not involving Quirrell is the most effective method of convincing targets that someone other than Quirrell is doing this? Perhaps Hat-and-Cloak's secrecy is to normal people what Quirrell's brilliance is to Harry (convincing), and Voldemort thinks or know that Quirrell can't pull off being H-&-C properly? Perhaps Quirrell is monitored in some way that he can't safely or nonsuspiciously avoid (I can believe Dumbledore setting up some such thing) and so Voldemort does just enough to fly under the "openly hostile" rader, using Hat-and-Cloak to strike the tinder as it were?
I don't know, but I suspect that if my claim is the case, the answer to your question is a reason the story itself does not reveal.
He certainly does the lion's share. Perhaps Hat-and-Cloak only handles less challenging or less dangerous-to-fail situations.
I was under the impression that Quirrellmort's zombie-time meant that the Quirrell host-body had been lobotomized. If so, any intelligence that Voldemort can bring to bear is already native to him. Of course, there is that comment in one of his early discussions with Harry about never being able to fully disentangle the mind from the body that it wears...I'm not yet entirely sure what to think about this. I don't think we have any direct evidence that Voldemort can step out of Quirrell without great inconvenience.