The correct option is
C that
The given sentence suggests that the subject, the old lady knew all about the things occurring in the neighborhood. Thus, the answer must be a pronoun that points out to the incidents of the neighborhood, that is, the answer must be a demonstrative pronoun.
Option A is incorrect. 'what' is an interrogative pronoun and not a demonstrative pronoun. Thus, it is the incorrect answer.
Option B is incorrect. 'where' is also an interrogative pronoun and not a demonstrative pronoun. Further, 'where' is used to refer to places and not things or incidents. Thus, it is not the correct answer.
Option C is correct. 'that' is a demonstrative pronoun. Thus, it refers to the incidents taking place in the neighborhood, and therefore, is the correct answer.
Option D is incorrect. 'who' is also an interrogative pronoun and not a demonstrative pronoun. Further, 'who' is used to refer to people and not incidents or things. Thus, it is incorrect.