following the trends of modern usage , which of the following sentences is grammatically CORRECT? a) This is her. b) Please take care of whomever is waiting. c) Who are you waiting for ?d) Whom would you like to be if you weren't yourself.
To answer this question, I would really like to know what "the trends of modern usage" means to you, or what you believe these trends have been. I can only venture my view based on my own experience that these "trends" have been away from respect for the authority of the traditional, prescriptive rules of grammar and toward more of an "anything goes" approach to the notions of "correct grammar" and "proper English," which is certainly not to say that attention to nor reverence for the authority of the former principles have entirely disappeared.
Whether my interpretation of "the trends of modern usage" accords with yours, I can say with a fair degree of certainty that your sentences b) and d) would be rejected as, at the least, strange or "funny" by many English speakers and as truly grammatically incorrect by others, though many still might be so thoroughly impressed by the presence of the prestige form whom in both that they'd deem both sentences as "correct" if not downright aspirational models. In the case of b), the speaker/writer may have chosen whomever instead of whoever in the mistaken belief that the preposition of governs it, thereby requiring the objective form whomever rather than the subject form whoever (if he/she didn't succumb to the other unfortunate tendency to "dress up" forms of who pretty much wherever they occur as whom to make them sound "better"). While this is in fact in line with the rules of traditional grammar, actually in the sentence in question of governs not simply whomever but the entire clause whomever [sic] is waiting, and thus because "whomever" is the subject of this clause it should be whoever instead.
Similarly, in d) the use of whom rather than who may be another instance of "hypercorrection" since grammatically the "Whom" is said to originate in "deep structure" as the complement of be in a structure like you would like to be whom, but the problem here is that in normal declarative sentences with a form of be followed by a subject complement (e.g., Frank is a lawyer, She was the queen), the subject complement is by definition equal in status to the actual subject noun phrase and thus like it should appear in the subjective form. That is to say, the true "deep structure" of d) is (at least in one stage of it, anyway) you would like to be who, with the who then "moved"--unchanged--to the front of the surface question yielding the grammatical Who would you like to be if you weren't yourself?
That leaves a) and c), and the explanation of the grammaticality of c) actually can employ a similar analysis as I gave for sentence d) above, namely that the who originates in deep structure as the sole object of the preposition for, i.e., you are waiting for who, but again as per the prescriptive rule I mentioned in my discussion of b) above, since who is the "object" of for it should properly be whom, and this is what should be "moved" to the front of the question yielding Whom are you waiting for? But the problems is that in any corpus of Modern English I would bet the farm that the occurrences of Who are you waiting for? would outnumber those of Whom are you waiting for? by about 99 to 1 since, as we all know, the word whom is pretty much moribund, if not already flatlined, in English, despite the efforts of the small group of people I mentioned in my first paragraph above to preserve it.
So finally we come to a), and this is indeed a similar case to c) in that what most of the grammar and writing handbooks say to use in such a sentence versus how it actually comes out in normal language are quite at odds. This sentence actually has a structure identical to the "deep structure" of part of d) as I analyzed it above, i.e., in the pattern This is X, X is again a subject complement and thus in traditional analyses "requires" the subject form. The clash between grammar dictates and actual usage here arises because the subject complement is a pronoun, namely her, which would then be "incorrect" in this sentence since, as mentioned, we would need the subject form of this pronoun instead which is of course she. And again, a sentence like This is she would probably be an even greater rarity in any corpus of our language than Whom are your waiting for?, and indeed anyone presumptuous enough to utter "This is she" in most normal conversational contexts would likely be immediately regarded as "putting on airs," if not evincing symptoms of mental illness, which might be a fine qualification to be a professional grammarian but hardly one that would endear you to others in the majority of social situations.