The correct sentence should be:

The song was so moving that all eyes became wet.

Explanation: The subordinating conjunction "that" is needed to connect the two clauses in the sentence. It indicates the cause-and-effect relationship between the moving song and the teary-eyed reaction.

The correct sentence should be:

Ariel was convinced that something fishy was going on behind his back.

Explanation: The verb tense in the reported speech should be consistent, so "is going" should be changed to "was going." Additionally, the preposition "on" should be replaced with "behind" for the sentence to convey the intended meaning.

The original sentence is grammatically correct and conveys its intended meaning effectively. There is no need for substitution or improvement in the underlined segment. 

An adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, etc. The adverb 'there' is used to introduce the subject of a sentence, especially before the verbs be, seem, and appear. Example: There seemed to be a problem with finding a date for the meeting. Hence in the given underlined part of the sentence, the correct choice will be the 1st option i.e. There is a hole.

The correct sentence is:

I will accept the responsibility when the time comes.

Explanation: In this sentence, "while" should be replaced with "when" to indicate a specific point in time. Additionally, "a" should be inserted before "time" to make the sentence grammatically correct.

The correct sentence is:

There was an argument about whether we should move to another city.

Explanation: In this sentence, "if" should be replaced with "whether" to introduce a indirect yes-no question. Additionally, "shall" should be replaced with "should" to form a correct conditional statement.

The correct sentence is:

The place was not only cold but also damp.

Explanation: In this sentence, the use of "only" and "also" is redundant. Instead, "not only...but also" is the correct correlative conjunction to use. Also, the conjunction "and" should be replaced with "but" for proper contrast between the coldness and dampness of the place.

The correct sentence is:

Many a person is unable to distinguish right from wrong.

Explanation: "Many a person" is a singular phrase and should be followed by a singular verb, which is "is" in this case. Additionally, the preposition "of" should be replaced with "to," and the article "the" is needed before the noun "right."