Does an AQP line check conducted by a part 121 carrier count as a flight review and instrument proficiency check for part 91 operations?
It depends if the AQP qualifies as a pilot proficiency check.  Most likely the the outcome will be a pilot proficiency check.


  §61.56   Flight review.
  
  
    ... 
    
    (d) A person who has, within the period specified in paragraph (c) of this section, passed any of the following need not accomplish the flight review required by this section:
    
    
      (1) A pilot proficiency check or practical test conducted by an examiner, an approved pilot check airman, or a U.S. Armed Force, for a pilot certificate, rating, or operating privilege.