Which of the following correctly applies to connotations ... They are always fixed, they are always subjective, or they can be fixed or subjective

Connotations can be fixed or subjective.

Connotations are the emotions that we associate with a given word. While most of the time, these are fixed (i. e. some words arouse pleasure while others contempt), they can be subjective. (i. e. for someone who is afraid of dogs, the word dog can imply danger, whereas for someone who loves dogs, the word can be a source of comfort and pleasure).