
Ed M. answered 02/11/16
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I would argue that all four of your statements could be true, given the proper interpretations of the term verb and the modal should. Taking the easier cases of sentences c) and d) first, should implies a normative judgement, i.e., a statement about how things ought to be but aren't necessarily so in the real world. So to say, for example, "A proper noun should begin with a capital letter" is to make a statement about a convention in Standard Written English--and one that I actually can't think of any exceptions to, by the way--that is in fact often "violated" in written forms of communication all the time; just look at any sample of text messages or online comments. Similarly, "When using coordinating conjunctions, you should join verbs with verbs, nouns with nouns,and [sic] so on" describes another convention of "good writing," i.e., parallelism, that most people do because they know it's something they "should," but sometimes it's not possible even for the best writers, e.g., when they need to coordinate things of different grammatical classes that resist reformulation into "parallel" structures. For example, one might write something like This is used for X and (for) Ying where X is a noun and Ying is the -ing form of a verb Y that the writer just can't think of an appropriate strictly noun form for to make it parallel with the noun X after the coordinating conjunction and.
As for your other two choices that both are about properties of a "verb," if one follows the modern practice of viewing a verb as not just a single word but as the actual realization of a number of grammatical and semantic elements all encapsulated below the surface as a verb phrase, then both a) and b) would be true also. Taking b) first because my answer to it will feed into my explanation of a), in a monster of a sentence like They will not have been being allowed, under many modern analyses all the six words of this sentence beyond the subject They are said to make up an entire verb phrase built around the main verb allow, which thus is described (by grammarians who would seem to have little else to do) as being in this case in the "negative future perfect passive progressive."
So if will not have been being allowed is considered one verb consisting of more than one word, thus making b) true, then a) is true also since some elements of a verb phrase can be contracted, as least in more informal varieties of English. Many contractions are of course of a subject and a verb, e.g., she's from she is or she has (when has is an auxiliary, not a main verb), and because the status of not as a component of the verb phrase is in fact controversial, we can overlook the numerous contractions of not with auxiliaries, e.g., hasn't and didn't, and instead take cases like You should've known where should've is a contraction of the modal should and the auxiliary have, both of which, as per the analysis referred to in the previous paragraph, would be considered parts of the verb phrase, i.e., the "verb" of the sentence, and because these can be contracted, your choice a) is arguably true also.