Learn English – “On which” or “upon which”

"To beg the question" means "to raise the question," or "to invite an obvious question."
From the context of that sentence, I would think that "beg the question" is used with the second meaning I reported.

The NOAD reports the following notes about the meaning of "beg the question":

The original meaning of the phrase beg the question belongs to the field of logic and is a translation of the Latin term petitio principii, literally meaning "laying claim to a principle" (that is, assuming something that ought to be proved first), as in the following sentence: "by devoting such a large part of the anti-drug budget to education, we are begging the question of its significance in the battle against drugs." To some traditionalists, this is still the only correct meaning. However, over the last 100 years or so, another, more general use has arisen: "invite an obvious question," as in "some definitions of mental illness beg the question of what constitutes normal behavior." This is by far the more common use today in modern standard English.

Methodology, n.:

1) the branch of philosophy that analyzes the principles and procedures of inquiry in a particular discipline

2) the system of methods followed in a particular discipline

While "discipline" seems to be used to refer to a field of expertise, rather than a particular task, I think you could stretch it to fit. But since you're not really analyzing the methods, and just mentioning them ("general overviews"), I would call the section Methods and not Methodology.

I think either methods or procedures would be appropriate terms, but not paradigms. A paradigm is best described as "a system of assumptions, concepts, values, and practices". Several methods could follow a particular paradigm, for example, but a paradigm is not a method itself.