- A noun phrase is a group of words that ends with a noun.
This definition is very approximate and I advise you to forget it if you wish to have at your disposal more useful describing terms. The following definition from the article in Wikipedia is an accurate global description (much more detail is necessary however to characterize fully these grammatical entities).
A noun phrase, or nominal (phrase), is a phrase that has a noun (or indefinite pronoun) as its head or performs the same grammatical function as a noun.
Noun phrases often function as
_ verb subjects,
_ predicative expressions,
_ the complements of prepositions.
Noun phrases can be embedded inside each other; for instance, the noun phrase some of his constituents contains the shorter noun phrase his constituents.
What is to be retained at first is that there is in a noun phrase an element that is the heart of the phrase, the head; this element is most often a noun but it can also be a pronoun. The elements other than the head can often be removed and a simpler noun phrase with the same head is obtained.
- He bought a ring made of gold.
The highlighted element in this sentence is not a noun phrase because it contains a verbal form that has the value of an adjective that does not modify anything in the group of words considered, and this highlighted element is therefore an adjectival phrase. The only noun phrase that can be extracted from this group is "gold"; "of gold" is a prepositional phrase.
Your first conclusion is then correct.
- A prepositional phrase is a group of words that begins with a preposition and ends with a noun.
A prepositional phrase does begin with a preposition. Here is what the article on adpositional phrases from Wikipédia
Prepositional phrases have a preposition as the central element of the phrase, i.e. as the head of the phrase. The remaining part of the phrase is called the prepositional complement, or sometimes the "object" of the preposition. In English […] it takes the form of a noun phrase, such as a noun, pronoun, or gerund, possibly with one or more modifiers.
Concerning "He lives in the suburb of Dhaka." you say "But if we consider the meaning of the highlighted phrase, we can see that it is giving us more information about where the subject lives and this phrase should be an adverb phrase."; this is both a prepositional phrase and an adverbial phrase, that is a phrase that functions as an adverbial. The problem is in your assimilation of the basic grammatical notions: you are confusing "adverb", which is a category in the parts of speech (nouns, verbs, adjective, adverbs, etc.), and "adverbial", which is a "(grammatical) function" (subject, verb, object, complement, et.).
Notice that in this next sentence a similar prepositional phrase is a subject (ref.).
- In the washing machine is not a place to put your child.
There is no question of giving more importance to one thing rather than to another one.