Can you cut open a plastic junction box and just lay splices inside?
Red tag party, anyone?

Hoo boy, that installer needs to get knocked back to school with a Codebook!  What's in the photos alone violates several sections of the NEC, starting with 314.17(A) on the excessive openings for conductors:


  (A) Openings to Be Closed. Openings through which conductors enter shall be closed in an approved manner.


We then move on to 314.23, where the utter lack of box support strikes:


  314.23 Supports. Enclosures within the scope of this article shall be supported in accordance with one or more of
  the provisions in 314.23(A) through (H).


Note that nowhere in the subsections does it allow for a box to flop loose on some insulation, supported only by cabling that is not strain-relieved to the box by an approved means (such as a cord grip).

Also note the bulging box lids, which are indicative of a violation of the general provisions of 314.16:


  314.16 Number of Conductors in Outlet, Device, and
  Junction Boxes, and Conduit Bodies. Boxes and conduit
  bodies shall be of an approved size to provide free space
  for all enclosed conductors. In no case shall the volume of
  the box, as calculated in 314.16(A), be less than the fill
  calculation as calculated in 314.16(B). The minimum volume for conduit bodies shall be as calculated in 314.16(C).
  
  The provisions of this section shall not apply to terminal housings supplied with motors or generators.
  
  Informational Note: For volume requirements of motor or
  generator terminal housings, see 430.12.
  
  Boxes and conduit bodies enclosing conductors 4 AWG
  or larger shall also comply with the provisions of 314.28.


From there, we continue the party at 300.11(A) on support:


  300.11 Securing and Supporting.
  
  (A) Secured in Place. Raceways, cable assemblies, boxes,
  cabinets, and fittings shall be securely fastened in place.
  Support wires that do not provide secure support shall not
  be permitted as the sole support. Support wires and associated fittings that provide secure support and that are installed in addition to the ceiling grid support wires shall be
  permitted as the sole support. Where independent support
  wires are used, they shall be secured at both ends. Cables
  and raceways shall not be supported by ceiling grids.


and move on to 300.3(A) and (B) for the single wires run loose in the attic:


  300.3 Conductors.
  
  (A) Single Conductors. Single conductors specified in
  Table 310.104(A) shall only be installed where part of a
  recognized wiring method of Chapter 3.
  
  Exception: Individual conductors shall be permitted
  where installed as separate overhead conductors in accordance with 225.6.
  
  (B) Conductors of the Same Circuit. All conductors of
  the same circuit and, where used, the grounded conductor
  and all equipment grounding conductors and bonding conductors shall be contained within the same raceway, auxiliary gutter, cable tray, cablebus assembly, trench, cable, or
  cord, unless otherwise permitted in accordance with
  300.3(B)(1) through (B)(4).


Finishing things off, we can write the installer up for violating 110.12, including 110.12(A) specifically:


  110.12 Mechanical Execution of Work. Electrical equipment shall be installed in a neat and workmanlike manner.
  
  Informational Note: Accepted industry practices are described in ANSI/NECA 1-2010, Standard Practice of Good
  Workmanship in Electrical Construction. and other ANSI-
  approved installation standards.
  
  (A) Unused Openings. Unused openings, other than those
  intended for the operation of equipment, those intended for
  mounting purposes, or those permitted as part of the design
  for listed equipment, shall be closed to afford protection
  substantially equivalent to the wall of the equipment.
  Where metallic plugs or plates are used with nonmetallic
  enclosures, they shall be recessed at least 6 mm (1/4 in.)
  from the outer surface of the enclosure.