1)  Every Student must complete their homework on time.

  correct

  Every student must complete his/her homework on time

 Rule – every pronoun must agree with their antecedents

 2) Him and I went to the store.

 correct 

 He and I went to the store.

 3) She give the gift to John and I.

 correct 

 She give the gift to John and me.

 4) The cat licked it’s pawn

 correct 

 The cat licked its pawn

 Rule – Possessive Pronoun never use apostrophes (its ,your ,our)