The sentence is grammatically incorrect and error lies in option C. We need an objective form of pronoun "I" here and that will be 'me' in place of 'mine' (i.e. a possessive pronoun that belongs to me). Thus, replace 'mine' with 'me'.

The sentence is grammatically incorrect and error lies in option A.
The given sentence is in the simple present tense and elaborating on a scenario. Thus, replace ‘radiating’ with ‘radiate’ to make the sentence grammatically correct.

The sentence is grammatically incorrect and error lies in option D. The given sentence is in simple past tense and elaborating the incidence of encountering an injured child. Thus, replace ‘quicken’ with ‘quickened’ to make sentence grammatically correct.

The sentence is grammatically incorrect and error lies in option B. The injured soldier does not begin to warm (means having or producing a comfortable and agreeable degree of heat or imparting heat) himself, in spite of it, he began to worm (to move in a twisting or contorted motion, (especially when struggling)) himself. We need a verb 'worm' before preposition 'to'. Thus, replace ‘warm’ with ‘worm’.

The sentence is grammatically incorrect and error lies in option D. Lying would be contrary to the nature of priest thus, we need an apostrophe 's' to show its possession. Thus, replace 'priests' with "priest's".

The error is in option A of the sentence.

The error is because of the incorrect preposition 'at'. It should be 'on the one hand' to make the sentence grammatically correct. The phrase 'on the one hand' is used to introduce a statement that is followed by another contrasting statement which is typically introduced with on the other hand.

Hence, option A is the correct answer.

The error is in option C of the sentence because of the missing preposition.

It should be 'ability of heat-trapping' to make the sentence grammatically correct.

Hence, option C is the correct answer.

The error is in option B of the sentence.

The use of indefinite article (a) is erroneous. Rather, the definite article (the) must be used before 'earth' to make the sentence grammatically correct.

Hence, option B is the correct answer.

The error is in option B of the sentence.

The subject in the sentence is singular i.e. 'list', hence, the pronoun must also be singular. 'Those' is the plural form of 'that'. Therefore, 'those' must be replaced with 'that' to form a grammatically correct sentence.

Hence, option B is the correct answer.

The error is in option B of the sentence.

The use of indefinite article (a) is erroneous because it cannot be used before plural nouns. Rather, the definite article (the) must be used before 'opinions' to make the sentence grammatically correct.

Hence, option B is the correct answer.