Do I have to do all exercises during a checkride, even if I did them in a previous one?
Yes, if this is your initial rating on a Commercial certificate, you have to do all of that rating's required tasks. A checkride for a given certificate is always self-contained. In the case of an additional Commercial rating (ASEL, for example) you can refer to the appropriate "Additional Rating Task Table" and you'll see that some areas are already covered by the existing Commercial rating.

If you look closely, you'll notice that the PTS standards for the same maneuvers are more precise for Commercial than they are for Private. Notice that Steep Turns differ in both bank angle and execution technique:

Commercial (from FAA-S-8081-12C)


  Task A: Steep Turns (AMEL and AMES)
  
  References: FAA-H-8083-3; POH/AFM.
  
  Objective: To determine that the applicant:
  
  
  Exhibits satisfactory knowledge of the elements related to steep turns.
  Establishes the manufacturer’s recommended airspeed or if one is not stated, a safe airspeed not to exceed VA.
  Rolls into a coordinated 360° steep turn with at least a 50° bank, followed by a 360° steep turn in the opposite direction.
  Divides attention between airplane control and orientation.
  Maintains the entry altitude, ±100 feet, airspeed, ±10 knots,
  bank, ±5°; and rolls out on the entry heading, ±10°.
  


Private (from FAA-S-8081-14B)


  Task A: Steep Turns (AMEL and AMES)
  
  References: FAA-H-8083-3; POH/AFM.
  
  Objective: To determine that the applicant:
  
  
  Exhibits satisfactory knowledge of the elements related to steep turns.
  Establishes the manufacturer’s recommended airspeed or if one is not stated, a safe airspeed not to exceed VA.
  Rolls into a coordinated 360° turn; maintains a 45° bank.
  Performs the task in the opposite direction, as specified by
  the examiner.
  Divides attention between airplane control and orientation.
  Maintains the entry altitude, ±100 feet, airspeed, ±10 knots,
  bank, ±5°; and rolls out on the entry heading, ±10°.