Loganmule -- Your Section 10 is actually exactly what it means when people claim the Bible is inerrant. "Infallible" is the position that the Bible doesn't get history or science wrong.
That being said, there's another claim which always makes me nervous. That is the idea of the Bible being entirely culturally situated. Even if it's merely inerrant, or even slightly less than that, it still has a certain amount of authority, and we shouldn't be too quick to dismiss something merely on the grounds of 'well, that only applies to their cultural situation'. My general rule of thumb is that I feel free to disregard specific instructions if I can discern a general principle behind the specific instruction. A good example is the directions regarding how a woman ought to dress. This is pretty clearly culturally bound; but there's a general principle that people ought not to dress ostentatiously which is not so culturally bound.
However, this also means that if there's no such general principle behind it, I'm not going to reject it as merely a cultural artifact. A good example is the issue of woman pastors. There are statements in the Bible that seem to say that churches cannot have female pastors. Now, there are good arguments that these statements don't actually mean that. But a bad argument, actually for a number of reasons, is that this merely reflects a patriarchal cultural bias on the part of the authors. Because we take the Bible seriously, we ought to give its human authors the benefit of the doubt.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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