The correct sentence should be:

Monika has been learning French for a long time.

Explanation: The verb form "learn" should be changed to "learning," and the auxiliary verb "has been" should be used to indicate the ongoing action of learning that has been happening for a period of time.

The correct sentence should be:

If somebody attacks you, you need to be able to defend yourself.

Explanation: The verb "needs" should be changed to "need," and the word "be" should be included for the sentence to be grammatically correct. The corrected sentence indicates the necessity of being able to defend oneself if attacked.

The correct sentence should be:

The doctor bade me take the medicine immediately after breakfast.

Explanation: In this sentence, the base form of the verb "take" should be used after the verb "bade." The construction "bade me taking" is incorrect; it should be "bade me take" to convey the intended meaning.

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.