What percent of assistant professors generally receive tenure, and how does this percent vary depending on both school and field? Are new assistant professors more likely to receive tenure in an expanding field, like biology? And are they less likely (percentage-wise) to receive tenure at elite schools?
This is actually quite a difficult question to answer specifically. Here is a brief paper reviewing some of the reasons why good data is unavailable on even very basic questions, together with some references to what is available. In the U.S. case, everyone agrees that, in general, the higher-ranked one's university, the more difficult it is to get tenure. Departments at some elite schools are notorious for their unwillingness or inability to grant tenure to their junior faculty over a very long period—in some cases, decades. (Just last year in my own field, for example, one of the leading departments tenured one of its junior faculty for the first time in more than twenty years. This is an extreme example, but you get the point.) 

Beyond the well-known general patterns and the (sometimes widely-reported) particular horror stories, though, many very interesting questions remain difficult to address systematically—including your one about expanding versus stable fields. The question is complicated by the fact that the institution of tenure itself is changing, as is its role within the university. As Wikipedia notes, in the United States "The period since 1972 has seen a steady decline in the percentage of college and university teaching positions in the US that are either tenured or tenure-track. United States Department of Education statistics put the combined tenured/tenure-track rate at 56% for 1975, 46.8% for 1989, and 31.9% for 2005. That is to say, by the year 2005, 68.1% of US college teachers were neither tenured nor eligible for tenure; a full 48% of teachers that year were part-time employees.