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."

The correct sentence is:

We are coping with the problems to the best of our ability.

Explanation: The verb "coping" should be followed by the preposition "with," and the definite article "the" is necessary before the noun "problems." Additionally, the phrase "to the best of our ability" is a common idiomatic expression used to indicate doing something as well as one can.

The underlined segment in the given sentence does not need improvement. It is already grammatically correct and conveys the intended meaning effectively:

Explanation: The verb "has" is the correct form to use with the pronoun "she." The original sentence, "She are having," is grammatically incorrect.

If we go through the given statement, it is not correct since it does not make any sense. 

Though it may seem that with some changes, the sentence would imply something. 

Here, we have to understand the context of the statement which is talking about the action to be taken by the Union Minister against others. 

Now, coming to the options, Option 1 can be ruled out since it is clear that with this option being implemented, the resultant statement would not make any sense whatsoever.

With Option 2 also, the same may be said since it also does not make any sense.

Option 3 can be ruled out since it does imply anything.

Option 4 is the right pick since if we interchange the words according to this option, the resultant statement will make sense. 'Threatened' should be used along with the term 'legal action', and with further part of the sentence 'two newspapers' fitting in well. 

Correct sentence: Union minister M.J. Akbar threatened to take legal action against several women journalists who had accused him of sexual harassment at two newspapers where he had been the editor.

The underlined part of the sentence is grammatically incorrect. The preposition 'for’ used here is wrong. The correct preposition should be 'to’. 

Gauge means to judge or assess (a situation, mood, etc.). 

Hence 'assess’ is a synonym of 'gauge’. 

Both choices B and C are correct. Hence the correct answer is option 4.