Are the size and location of the registration number regulated?
Under FAA jurisdiction, these items are regulated under 14 CFR 45.

The size of the registration markings must generally be at least 12 inches high:


  §45.29
  
  (a) Except as provided in paragraph (f) of this section, each operator of an aircraft must display marks on the aircraft meeting the size requirements of this section.
  
  (b) Height. Except as provided in paragraph (h) of this part, the nationality and registration marks must be of equal height and on—
  
  (1) Fixed-wing aircraft, must be at least 12 inches high


The markings must be displayed on either the vertical tail surfaces or the sides of the fuselage.


  §45.25
  
  (a) The operator of a fixed-wing aircraft must display the required marks on either the vertical tail surfaces or the sides of the fuselage, except as provided in §45.29(f).
  
  (b) The marks required by paragraph (a) of this section must be displayed as follows:
  
  (1) If displayed on the vertical tail surfaces, horizontally on both surfaces, horizontally on both surfaces of a single vertical tail or on the outer surfaces of a multivertical tail.
  
  (2) If displayed on the fuselage surfaces, horizontally on both sides of the fuselage between the trailing edge of the wing and the leading edge of the horizontal stabilizer. However, if engine pods or other appurtenances are located in this area and are an integral part of the fuselage side surfaces, the operator may place the marks on those pods or appurtenances.


There are exceptions to these requirements, but these exceptions will not generally apply to the modern airliners referenced in your question.

While the regulations do not prohibit it, I think it would be unusual for the registration to be displayed in more than one location on a given side of the aircraft—for example, on both the tail and the fuselage.

Under ICAO requirements, these items are described under Annex 7.

Annex 7, paragraph 3.3.1 includes the additional requirement for heavier-than-air aircraft that the registration markings should be displayed on the lower surface of the wing structure. 


  3.3.1 Wings. On heavier-than-air aircraft the marks shall
  appear once on the lower surface of the wing structure. They
  shall be located on the left half of the lower surface of the
  wing structure unless they extend across the whole of the
  lower surface of the wing structure. So far as is possible the
  marks shall be located equidistant from the leading and trailing
  edges of the wings. The tops of the letters and numbers shall
  be toward the leading edge of the wing.


The FAA has no such requirement, but other jurisdictions do, such as the UK's CAA, which is effectively identical to the ICAO guidance.

The ICAO size requirements for heavier-than-air aircraft are similar to FAA requirements, with the obvious exception of the wing markings. These requirements are found in Annex 7, paragraph 4.2:


  4.2.1 Wings. The height of the marks on the wings of
  heavier-than-air aircraft shall be at least 50 centimetres.
  
  4.2.2 Fuselage (or equivalent structure) and vertical tail
  surfaces. The height of the marks on the fuselage (or
  equivalent structure) and on the vertical tail surfaces of
  heavier-than-air aircraft shall be at least 30 centimetres.


Note that 30 centimetres is approximately equivelant to 12 inches, and 50 centimetres is approximately equivelant to 20 inches.