Below are my thoughts about your questions on the prepositional phrases, the appositive, and the absolute phrase. Your questions are set in blue text; my answers, in black text.
Before reading this chapter, I had some idea about what a phrase is, but didn't know there were so many and what purpose they serve. If I understood it correctly, the many types of phrases are there to simply modify something else. This chapter served as a spring board for me to search on further. Very interesting stuff.
I have a few questions I'd like to ask regarding these phrases.
1) Prepositional Phrase - The woman, although uncomfortable with the idea, wore a starkly red dress and red high-heels to the costume party last night.
I initially thought the prepositional phrase was: "although uncomfortable with the idea" but although is a conjunction right? Does that make it a conjunction phrase if such exists?
Yes, “although” is a subordinating conjunction that means “in spite of the fact that” or “even though,” the phrase it introduces in that sentence is actually a subordinate phrase—not a conjunction phrase”—that modifies the noun “woman.”
2) I had gathered some examples (on the net) of an Absolute Phrase, (at least that's what the source claims to be as an absolute phrase) and then started thinking, "What makes an absolute phrase different from the other phrases that it bears resemblance to?"
a) The question still unanswered, , the teacher decided to address the confusion of her students more closely. (looks like a noun phrase)
No, “the question still unanswered” isn’t a noun phrase but an absolute phrase. It would be a noun phrase if it were in the form “a still unanswered question,” but it would have no business in that position in the sentence; in fact, it would be dangling noun phrase because it couldn’t logically modify the noun “teacher.”
b) There are many industries in California vital to its economy, with technology being one of the most important. (looks like a prepositional phrase)
Yes, “with technology being one of the most important” is a prepositional phrase in that sentence and it’s one that modifies the entire clause “there are many industries in California vital to its economy.” If we knock off the preposition “with” and the verb “being,” though, and move the phrase up front of the sentence, it would function as an absolute phrase, as follows:
“Technology one of the most important, there are many industries in California vital to its economy.”
c) Chosen to head the committee, Angus Ng thought about how he could help raise money for his chess club at Harvard. (looks like a participial phrase)
“Chosen to head the committee” indeed looks like a participial phrase, but it’s actually an absolute phrase crafted into one by removing the verb form “having been” in the participial phrase “having been chosen to head the committee.”
3) One website says that an appositive phrase is a noun-phrase that renames another noun.
If that is so, the following example should be correct:
# I took a cookie from Gretel, who is the woodcutter's daughter.
The author said that this isn't an appositive, but an adjectival phrase.
a) My basis for knowing if it is an adjectival phrase is to first look at the start of the phrase, if it starts with an adjective. If it's not that apparent, then I ask the subject: Which? (eg. Which Gretel?) or what kind. The phrase doesn't fit.
Yes, the author is right in saying that in that sentence, “who is the woodcutter’s daughter” is an adjectival phrase modifying the noun “Gretel”; it’s also a nonrestrictive noun phrase modifying “Gretel.” Adjectival phrases like that become appositives when we knock off the relative pronoun “who” and the linking verb “is,” as follows:
“I took a cookie from Gretel, the woodcutter's daughter.”
b) This looks like a noun phrase to me, since it begins with a pronoun, "who" as noun phrases can have pronouns at the head of the phrase right?
c) If this is so, then can this also be considered an appositive? if not, what kind of phrase is this?
# I took a cookie from Gretel, the woodcutter's daughter.
The website said that this is the correct answer, and based on other examples I gathered from other websites, they all followed a similar structure with the example you shared (The woman, a stunning beauty with a rebellious streak, wore a starkly red dress and red hihg-heels to the costume party last night).
Other examples:
a) The insect, a cockroach, is crawling across the table.
b) Reliable, Diane's eleven-year-old beagle, chews holes in the living room carpeting as if he were still a puppy.
c) Upset by the bad call, the crowd cheered Robbie, a hot-tempered tennis player who charged the umpire and tried to crack the poor man's skull with a racket.
So in this case, this is an appositive, modifying Gretel as an adjective, and not an adjectival phrase. Am i right or am i just confusing myself?
In the three examples you gave above, all of the underlined phrases are appositives—not adjectival phrases. They were originally adjectival phrases, but they became appositives when their respective relative pronouns “who” or “which” and linking verb “is” were knocked off.
For instance, in the sentence "I took a cookie from Gretel, who is the woodcutter's daughter," the adjectival phrase "who is the woodcutter's daughter" becomes the appositive "the woodcutter's daughter" when the words "who" and "is" are knocked off. The resulting sentence will be as follows: "I took a cookie from Gretel, the woodcutter's daughter."
4) How do we differentiate a Participial from a Gerund phrase? The Gerund phrase looks very similar to the present participle of a verb.
Example for Participial Phrase:
Feeling uncomfortable about the whole thing, the woman wore a starkly red dress and red high-heels to the party last night.
Example for Gerund Phrase:
Wearing a starkly red dress and red high-heels was the woman's idea of getting attention during the costume part last night.
A participial phrase acts as an adjective modifying a noun in the sentence, as in “feeling uncomfortable about the whole thing” modifying “the woman” in the first example above. On the other hand, a gerund phrase acts as an noun serving as a subject or doer of the action in the sentence, as in “wearing a starkly red dress and red high-heels” acting as the subject in the second example above.
5) Since the phrases serve to put the emotional texture into an otherwise non-descript narrative or extemporaneous speech, as far as knowing the "technical names" for the phrases, is it the kind of information that is --good to know from a teaching standpoint or should we try to keep the technical names in mind as we formulate our thoughts even in free speech?
It would be nice to know the technical names of the various types of modifying phrases from the standpoint of learning how they work grammatically and where and when they can best be used, but we need not be overly conscious about them when we are in the act of writing. The best way to write is to make our thoughts flow as naturally and spontaneously as possible. Only after we are done with the written piece should we start to ruthlessly edit it for grammar, logic, parallelism, balance, and consistency of style.