Using げ to turn adjectives and nouns into adverbs

Question

「自慢げに話す」「得意げに話す」「誇らしげに話す」

Is this げ a simple way to turn adjectives and nouns into adverbs? (are the first two examples nouns turned into adverbs, or were they adjectives as well to begin with?)

Answer 1

～げ, although usually written with hiragana, can also be written as ～気, and means something like "have an air of...". These can be used as na-adjectives:

自慢げな態度 an attitude with an air of boastfulness
得意げに話す speak with an air of (over-)confidence
悲しげな顔 a face with an air of sadness

Some can also be used as nouns, but beware, not all of the ones that can be used as na-adjectives are used as nouns. The nouns are most commonly used with ない (but other uses also occur).

大人{おとな}げ(が)ない immature (no air of matureness)
かわいげ(が)ない impertinent (lit. no air of cuteness)

Answer 2

自慢　is a suru-noun, 得意 is an adjectival-noun (na-adjective), and 誇らし is the root of an i-adjective. I think げ turns them all into adjectival-nouns. A clear diagnostics is that you can create the attributive form with な.

自慢げな態度
得意気な態度
誇らしげな態度