What is the syntactic function of the noun phrases above in their respective clauses (see text)? a) The media is one of...

 Syntax refers to the arrangement of different parts of speech according to a set of rules about patterns and order. That is, in English syntactical function refers to the grammatical constructions of words and their arrangement in a sentence. For, as a syntactic language, English makes use of this system of ordering words (especially nouns) to indicate relationships that convey meaning. (Other languages sometimes change the spelling of nouns in order to convey meaning or case, a process called declension.)

Here is the syntactic function of the following noun phrases given above: 

(a) (This one has been completed as described above.)

(b) The most important thing is to decide what the purpose of the interview is for you.

This sentence is also a simple sentence composed of one main clause. The syntactic function of the words in bold is that of the subject of the sentence. The noun thing is the simple subject, and "The most important" modify this subject. [The=an article, most=adverb of degree which qualifies important, and important = an adjective]

(c)  If another colleague is better than you on television and radio, then push him or her forward. 

This is a complex sentence (an independent clause and a subordinate clause=a complex sentence). another colleague functions as the subject of the subordinate clause which begins with the subordinating conjunction if. [another=adjective, colleague=noun]

(d)  You should insist on meeting the other people involved before the discussion starts.

Since "the other people involved" is all in bold together, the implication here is that "involved" is attached to people as a past participle acting as a limiting adjective for this noun. The words in bold are part of a participial phrase:"meeting the other people involved." 
Therefore, the syntactical function of the words in bold are as the object of a participle. (meeting the other people involved = a participial phrase.)  As verbals, participles can take objects. [http://grammar.about.com/od/pq/g/partphraseterm.htm}

(Note: Qualifying the type of sentence is a little tricky because traditionalists may argue that this sentence is elliptical because who are is understood, not stated, after the word people and, therefore, begins a subordinate clause. So, according to this argument, the sentence can be read as a complex sentence, rather than a simple sentence with only one main clause as it appears to be when read with "involved" as past participle used as an adjective.)