In general, this is explained when bringing up Occlumency in the first place. If he was good enough, he could readily agree to dropping his shields, then just keep them up. How would they tell? Again, this is assuming that he's good enough, but it does mean that they could never be certain. If they were motivated enough, they could Imperios to make sure he actually did it, but it is an Unforgivable...
1) I agree w/ JoshuaZ, Dumbledore might not want to further antagonize Harry w/o quite possibly gaining anything from it. It might be worth the risk, though.
2) That is quite possible, but I think that Snape's biggest hurdle in this is that he is still seriously underestimating Harry. Though the fact that Quirrell had to deduce that the girl had a Time Turner, and not just know, means that he possibly wouldn't know that there's a Slytherin w/ a Time Turner, or even necessarily that there are any issued at the moment. He could, through checking his student's schedules, but he might not know offhand.
3) I really wouldn't say an order of magnitude smarter than Dumbledore, he's just tuned his mind to that kind of thinking through decades of experience. Again, I agree w/ JoshuaZ in that Moody wouldn't be thinking of him as an option. He honestly might not even know the information that would be required for him to make that deduction, like Harry's predilection for Muggle artifacts.
edit: I forgot to say, I did not think of the animagus potion as evidence of Harry's innocence, but rather of Voldemort's guilt. Rather than making Harry less likely, it merely makes Voldemort more likely.
Harry isn't good enough to fool Dumbledore's Legilimency, and he knows that. See Ch. 58:
He had decided to keep the memories. For one thing, they were important. For another, he and the Defense Professor had started planning this a week ago, and Harry wasn't about to obliterate the whole last week, or explain to Bellatrix exactly what needed to be Obliviated. Harry could probably fool Veritaserum, and if Dumbledore insisted that Harry drop his Occlumency shields for a deeper examination... well, Harry had acted heroically throughout.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
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: