Well I would say 4 days of searching by the USCG sounds pretty thourough. These reports follow a standard format and only if a new technique was used would the search be detailed. 4 days would allow enough time for surface ships to be used.
As for the operator continuing to search after the govt have stopped - not unusual.
As for ELT? Again seems reasonable, the answer to the next 2 questions ELT activated and ELT assisted in search are definately NO so the answer to the question ELT fitted would have to wait until the wreckage could be examined. Only there is no wreckage.