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Nice try. You've almost succeeded at summarizing practically all the relevant arguments against the SI initiative that have already been refuted. Notice the last part there that says "have already been refuted".
Each of the assertions you make are ones that members of the SI have already adressed and refuted. I'd take the time to decompose your post into a list of assertions and give you links to the particular articles and posts where those arguments were taken down, but I believe this would be an unwise use of my time.
It would, at any rate, be much simpler to tell you to at least read the articles on the Facing the Singularity site, which are a good vulgarized introduction to the topic. In particular, the point of timescale overestimates is clearly adressed there, as is that of the "complexity" of human intelligence.
I'd like to also indicate that you are falsely overcomplexifying the activity of the human brain. There are no such things as "numerous small regions" that "run programs" or "communicate". These are interpretations of patterns within the natural events, which are simply, first and foremost, a huge collection of neurons sending signals to other neurons, each with its own unique set of links to particular other neurons and a domain of nearby neurons to which it could potentially link itself. This is no different from the old core sequence article here on LessWrong where Eliezer talks about how reality doesn't actually follow the rules of aerodynamics to move air around a plane - it's merely interactions of countless tiny [bits of something] on a grand scale, with each tiny [bit of something] doing its own thing, and nowhere along the entire process do the formulae we use for aerodynamics get "solved" to decide where one of the [bits of something] must go.
Anyway, I'll cut myself short here - I doubt any more deserves to be said on this. If you are willing to learn and question yourself, and actually want to become a better rationalist and obtain more correct beliefs, the best way to start is to go read some of the articles that are already on LessWrong and actually read the material on the Singinst.org website, most of which is very readable even without prior technical knowledge or experience.
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None of that fog obscures the basic fact that the number of feminist female bank tellers cannot possibly be greater than the number of female bank tellers. The world is complex, but that does not mean that there are no simple truths about it. This is one of them.
People have thought up all manner of ways of exonerating people from the conjunction fallacy, but if you go back to Eliezer's two posts about it, you will find some details of the experiments that have been conducted. His conclusion:
The conjunction error is an error, and people do make it.
I reread that section, and you are correct, given that they don't tell you whether or not she is a feminist, it cannot be used as a criterion to determine whether or not she is a banker. However, I would say that the example, in typical public education style, is loaded and begs an incorrect answer. Since the only data you are given is insufficient to draw any conclusions, the participant is lead to speculate without understanding the limitations of the question.
As for "utility function", there are at least three reasons why it is not just wrong, but entirely impossible.
1: Utility is heterogeneous. Which gives you more "utility", a bowl of ice cream or a chair? The question itself is nonsensical, the quality/type of utility gained from a chair and a bowl of ice cream are entirely different.
2: Utility is complementary. If I own a field, the field by itself may be useless to me. Add a picnic table, and some food and suddenly the field gains utility beyond the food, table, and field individually. Perhaps I could run horses through the field, or add some labor and intelligent work and turn it into a garden, but the utility I get from it depends on my preferences (which may change) and the combination with other resources and a plan. Another example, a person who owns a yaht would probably get more "utility" out of going to the ocean than someone who does not.
3: Utility is marginal. For the first three scoops of ice cream, I'd say I get equal "utility" from each. The fourth scoop yields comparably less "utility" than the previous three, and by the fifth the utility becomes negative, as I feel sick afterwards. By six scoops I'm throwing away ice cream. On the other hand, if I have 99 horses, whether I gain or lose one would not make much difference as to the utility I get from them, but if I only have 2 horses, losing one could mean losing more than half of my utility. Different things have different useful quantities in different situations depending on how they are used.
4: Utility cannot be measured. This should be obvious. Even if we were to invent a magical brain scanner that could measure brain activity in high resolution in vivo, utility is not always the same for the same thing every time it is experienced, and you still have the apples-oranges problem that makes the comparison meaningless to begin with.
5: Human psychology is not a mere matter of using logic correctly or not. In this case, it is definitely a misapplication, but it seems the only psychology that gets any attention around here is anecdotes from college textbooks on decisions and some oversimplified mechanistic theorizing from neuroscience. You talk about anchoring like it's some horrible disease, when it's the same fundamental process required for memory and mastery of concepts. You've probably heard of dissociation but you probably wouldn't believe me if I told you that memory can be flipped on and off like a light switch at the whim of your unconscious.
That aside, treating intelligence as a machine that optimizes things is missing the entire point of intelligence. If you had ever read Douglas Hofstadter's "Godel Escher Bach", or Christopher Alexander's "The Nature of Order" series, you might have a greater appreciation for the role that abstract pattern recognition and metaphor plays in intelligence.
Finally, I read two "papers" from SI, and found them entirely unprofessional. They were both full of vague terminology and unjustified assertions and were written in a colloquial style that pretty much begs the reader to believe the crap they're spewing. You get lots of special graphs showing how a superhuman AI would be something like two orders of magnitude more intelligent than humans, but no justification for how these machines will magically be able to produce the economic resources to reach that level of development "overnight". Comparing modern "AIs" to mice is probably the most absurd fallacy I've seen thus far. Even the most sophisticated AI for driving cars cannot drive on a real road, its "intelligence" is overall still lacking in sophistication compared to a honey bee, and the equipment required to produce its rudimentary driving skills far outweigh the benefits. Computer hardware may improve regularly by Moore's Law, but the field of AI research does not, and there is no evidence that we will see a jump in computer intelligence from below insects to above orangutans any time soon. When we do, it will probably take them 50-100 years to leave us fully at orangutan level.