1. Option C is incorrect because because, although it does not contain a grammatical error, it does not quite make sense. The reason for this lies in the verb DISCOVERED and in the nature of the thing discovered. Had the sentence said that the teacher discovered a stash of marijuana, it would have been fine, just as it would have been if it had said that he or she discovered a lost piece of jewelry. In other words, the teacher in both cases discovered an identifiable, specific substance or object. Nevertheless, this is not the case in Option C. INVOLVEMENT is something abstract (as is the subsequent ABUNDANCE): what the teacher discovered was not the INVOLVEMENT itself or the ABUNDANCE itself but rather the fact that THE INVOLVEMENT WAS LIMITED and the fact THAT AN ABUNDANCE (of administrative hassle) EXISTED. One can no more discover INVOLVEMENT or ABUNDANCE than one can discover DISAPPOINTMENT or DELIGHT or EFFORT. One can, however, discover that these things exist or that they are common or limited or absent.

2. In respect of your question about what THERE refers to, the answer is that it refers to nothing. When used as it is in this example, THERE is what is called an expletive pronoun. (Sometimes it is called a dummy pronoun.) An expletive pronoun has no referent. In the sentence There are fewer and fewer tigers in India, the subject is TIGERS, and for this reason the verb is plural: ARE. The expletive pronoun is used simply as a kind of grammatical 'filler' to satisfy the requirement In English that a verb be preceded by a subject - or, as in this case, by a pseudo-subject.

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