According to the Boeing documents, the ground power receptacles are below the 1L door. The ground service locations can be found on the Boeing web site
http://www.boeing.com/assets/pdf/com...ps/787sec5.pdf This is used by airport designers for setting out the service points on the apron. The distributed design on the 787 electrical system can also be found on-line. A photo on BBC news clearly shows that both sides are physically connected.
The access panels can be seen to be open on both sides, with the ground power cables hanging down. This would seem to be a fixed installation. behind the nose gear appears to be a cart, with an articulated cable system. The ground power converters appear to be at the base of the apron flood light masts. These would be fixed regulated solid state systems converting from 415V 50Hz to 110V 400Hz. Clearly from the photos, it is not possible to see if they are energized. There does not appear to be a tow tug or tow bar in the photo, so either they got out sharpish, or discussion about towing is not relevant.
The ground power requirement is rated at a nominal 90kVA at 110V 400Hz. Each connection can provide up to 1100 Ampere. For a typical turn around, both sockets at the nose will be connected. On a stand, they would normally be used until the APU is started. If there are any activities on the aircraft, such as cleaning or maintenance on board, it is likely that cabin lighting would be on as a minimum.
I think the concern for the industry and passengers would be if it is normal and acceptable for an overheating water heater / failing cabin air fan / discarded cigarette / overheating phone on charge / overloaded panel board to burn through the skin so quickly. Hopefully there will be a recording of voltage and electrical load conditions leading up to and during the event for analysis. This may show an event which can be used to time stamp the time of the failure. Clearly there will be no black box (FDR) recording, without the engines running, however the power system has limited data logging. One of the concerns of the NTSB in the previous battery investigation, was a lack of confidence in recorded voltage values.
I cannot claim expertise on aircraft structural repairs, although I do recall a very interesting documentary on National Geographic that had a film crew following the replacement of the rear pressure bulkhead in a 767. To summarise, everything behind the bulkhead was lifted off by crane. I presume that the photo previously posted was of the rear fuselage section on a transport jig. Aircraft sections are routinely shipped for bringing together at final assembly. If the rear pressure bulkhead is compromised, what is the chance that one of these is already being prepared for shipping to Heathrow?