Is there any sort of expert matching on Stack Overflow? Does SO take any implicit measures of expertise to influence how it distributes questions? Do newbie questions go to the same users as questions that would require a lot of expertise to answer?
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No, all questions go to all people who want to see them.
In other words, questions aren't sent to anyone. Users can view and answer any question that is posted. Most "expert" users will generally focus their attention on questions with a particular set of tags, so be sure to tag your question appropriately for what topic(s) it covers.
People just find the questions they want to answer. The questions on the active tab are just those with recent edits or answers. The only way people are given questions they are best-equipped to answer is ability to set interesting and ignored tags.