What is the structure of the crew documentation used in flight for a commercial aircraft?
The documents legally required on-board differ by jurisdiction. I can only speak to the case here in the US which falls under the FAA. If the flight is between two jurisdictions there may be local regulations to comply with at your destination as well. For example if leaving the US all onboard must have their passports as well as any pertinent custom forms.   


  What are they used for?


Generally these documents are all used for reference. Here in the US its generally forbidden to read personal material in the cockpit however the pilots are free to read documentation relating to the aircraft and operations. They may chose to use time in flight to read up on things.

These documents also include emergency procedures that the crew may need to use in the event of a failure.   


  What are the other major documents necessary to fly?


Aside from what the plane needs the crew must also have current medical certificates and pilots license on their persons.

If we take a look at FAR 121.135


  (a) Except as provided in paragraph (c) of this section, no
  certificate holder may operate an aircraft unless that aircraft— 
  
  
    (1)
    Is registered as a civil aircraft of the United States and carries an
    appropriate current airworthiness certificate issued under this
    chapter; and 
    
    (2) Is in an airworthy condition and meets the applicable
    airworthiness requirements of this chapter, including those relating
    to identification and equipment. 
  
  
  (b) A certificate holder may use an
  approved weight and balance control system based on average, assumed,
  or estimated weight to comply with applicable airworthiness
  requirements and operating limitations. 
  
  (c) A certificate holder may
  operate in common carriage, and for the carriage of mail, a civil
  aircraft which is leased or chartered to it without crew and is
  registered in a country which is a party to the Convention on
  International Civil Aviation if— 
  
  
    (1) The aircraft carries an
    appropriate airworthiness certificate issued by the country of
    registration and meets the registration and identification
    requirements of that country; 
    (2) The aircraft is of a type design
    which is approved under a U.S. type certificate and complies with all
    of the requirements of this chapter (14 CFR Chapter 1) that would be
    applicable to that aircraft were it registered in the United States,
    including the requirements which must be met for issuance of a U.S.
    standard airworthiness certificate (including type design conformity,
    condition for safe operation, and the noise, fuel venting, and engine
    emission requirements of this chapter), except that a U.S.
    registration certificate and a U.S. standard airworthiness certificate
    will not be issued for the aircraft; 
    (3) The aircraft is operated by
    U.S.-certificated airmen employed by the certificate holder; and (4)
    The certificate holder files a copy of the aircraft lease or charter
    agreement with the FAA Aircraft Registry, Department of
    Transportation, 6400 South MacArthur Boulevard, Oklahoma City, OK
    (Mailing address: P.O. Box 25504, Oklahoma City, OK 73125).
  
  
  Do they differ with manufacturers or airlines?


Airlines may publish excess documentation and checklists that meet or exceed the manufacture specifications this some airlines may have slightly varying procedures. Aircraft makers must publish documentation for the aircraft that includes its operational limitations you can find a good chunk of the regulations in the FAR's here. Specifically, 


  §23.1581   General.
  
  (a) Furnishing information. An Airplane Flight Manual must be
  furnished with each airplane, and it must contain the following:
  
  (1) Information required by §§23.1583 through 23.1589.
  
  (2) Other information that is necessary for safe operation because of
  design, operating, or handling characteristics.
  
  (3) Further information necessary to comply with the relevant
  operating rules.
  
  (b) Approved information. (1) Except as provided in paragraph (b)(2)
  of this section, each part of the Airplane Flight Manual containing
  information prescribed in §§23.1583 through 23.1589 must be approved,
  segregated, identified and clearly distinguished from each unapproved
  part of that Airplane Flight Manual.
  
  (2) The requirements of paragraph (b)(1) of this section do not apply
  to reciprocating engine-powered airplanes of 6,000 pounds or less
  maximum weight, if the following is met:
  
  (i) Each part of the Airplane Flight Manual containing information
  prescribed in §23.1583 must be limited to such information, and must
  be approved, identified, and clearly distinguished from each other
  part of the Airplane Flight Manual.
  
  (ii) The information prescribed in §§23.1585 through 23.1589 must be
  determined in accordance with the applicable requirements of this part
  and presented in its entirety in a manner acceptable to the
  Administrator.
  
  (3) Each page of the Airplane Flight Manual containing information
  prescribed in this section must be of a type that is not easily
  erased, disfigured, or misplaced, and is capable of being inserted in
  a manual provided by the applicant, or in a folder, or in any other
  permanent binder.
  
  (c) The units used in the Airplane Flight Manual must be the same as
  those marked on the appropriate instruments and placards.
  
  (d) All Airplane Flight Manual operational airspeeds, unless otherwise
  specified, must be presented as indicated airspeeds.
  
  (e) Provision must be made for stowing the Airplane Flight Manual in a
  suitable fixed container which is readily accessible to the pilot.
  
  (f) Revisions and amendments. Each Airplane Flight Manual (AFM) must
  contain a means for recording the incorporation of revisions and
  amendments.
  
  Are they available on paper or display?


Depends on the carrier, a great deal of movement to iPads and the such has seen the digitization of many things.