In the above underline, two error of appropriate pronoun usage occurs.

 He                   resented                   them criticizing their efforts

Subject          +              Verb                    +                Object (In the form of phrase)

Error occurs in Object, where the word ‘them’ will be ‘their’ as ‘criticizing’ is gerund (verb+noun). In that sense only possessive form of a noun (their) can modify another noun (criticizing).

Another error is ‘their’ that will be replaced with ‘his‘ as the word represents the subject ‘He’.

He                   resented                    his efforts

Subject          +            Verb                    +                Object 

Error occurs in usage of appropriate form of preposition (her).

Any gerund (entering) preceding by pronoun, must be in the possessive form (your).

    your                           entering

Possessive form            +            Gerund

In the above underline, ‘I' should be me.

As any word/s after preposition is the object of that preposition.

So, ‘I’ should be replaced by ‘me’.

                of                                                 Rose and me

               Preposition                  +                 Object (Pronoun would be in objective form)

Here, three small sentences exist in the above complex sentence.

1.       The man                                                                                     could not win    the game    at last.

            Subject                                                     +                                                                               Verb        +         Object    +      Modifier

2.                         whom                            would win        the game

                          Subject                       +                      verb            +         object

3.                                     I             thought

                                               Subject      +        Verb

 From the above structure, it is clear that ‘whom’ is the subject of ‘would win’, but the word ‘whom’ is not subjective form. The word should be substituted by subjective form ‘who’.

The main part of the sentence:

Everything          depends          upon him arriving ……

      Subject        +        Verb            +               Object

From the above structure, only fault is in object.

                upon                                  him arriving

            Preposition                  +         Object (Pronoun would be in objective form)

Any preposition (him) before gerund would be in possessive form (his).

and 'the guilty persons' ………… refers to…….. 'his' punishment.

Here, ‘his’ should be ‘their’ as ‘their’ denotes ‘the guilty persons’.

The structure of the sentence:

     He     + was told to give + the award + ……………....

  Subject                      Verb                      Object (Objective clause)

……+ whomever + he thought + had done + ………..

                  Subject                 Absolute                  Verb                   

                                                       Objective clause

From the above sentence structure, it is clear that ‘whomever’ is the subject of the verb ‘had done’. So subjective form (whoever) should be replaced instead of ‘whomever’.

And ‘he thought’ is the absolute that, if omitted, doesn’t make any distort of meaning as well as basic sentence structure.

In the above complex sentence two separate sentence is adjoined with subordinate conjunction ‘because’. The underline sentence is subordinating clause as it narrates the additional meaning of the main clause.

The error in the subordinating clause is known as ‘error of parallelism’.

Because of   +   its simple method of presentation +  and  +   because it is cheap.

                                                            Noun phrase                                                                Clause

But after the conjunction ‘because’ both should be similar in structure-either in phrase or clause form. So, option (D) is the best.

Here, we can see the ‘error of parallelism’ in the above underline.

Not only regressive but also because of being unnecessary.

                 Adjective                                                    Phrase

Rather, after ‘but also’ it should adjective instead of phrase.

Not only regressive but also unnecessary.

                 Adjective                            Adjective

country ban investments there and numerous goods may not be imported

                                         Noun                                                                 Clause

To maintain the parallelism of object and modifier, the clause after coordinating connective (and) should also be noun.

So, the choice-(A) is appropriate and precise to express the meaning.

country ban investments there and importation of numerous goods.

                                         Noun                                                  Noun (Noun phrase)

The main structure of the sentence:

                                            has discovered the need to conserve energy.

                   The world community   +                          Active form

         Subject                                   attempts have been made to meet the crisis.

                                                                      Passive form

Here, two independent clauses connected with coordinating conjunction (and); one in active form and the other in passive form. The passive form has been made unnecessarily.

As the clauses are connected with coordinate, structure of the clauses should be parallel.

                                                has discovered the need to conserve energy.

The world community   +                          Active form

         Subject                                         has made attempts to meet the crisis.

                                                                      Active form

So, choice –(B) is appropriate.