CBR is not an international destination normally, so no customs. I would imagine that that is the case in the US, as well as every other country in the world. However, customs are available for charters, etc if arranged in advance. As for diversions, my understanding is that customs are available on a call out basis. Don't know how long it takes to get them there, but I would imagine that it would be a while. It would probably cost a bit for an aircraft that size as well. I know it would seem a little strange that a nation's capitol does not have an international airport, but that is the way Australia has developed. There is plenty of information available on how the capitol ended up at Canberra, rather than Sydney (or even Melbourne), so if you are wondering, look it up.
As for the runway, witwiw has a good point. Only one of the three runways would have been closed. Admittedly, 07/25 would not have been available except in an emergency, due to the north/south runways being in use. However, 16L has 2200m for landing & 34R has 2400m for landing, so a B777 could land on 16L/34R with no problems, particularly a -200.
It was their choice to divert to CBR & they should have known about the limitations of the airport (read your manuals!). So don't carry on about the supposed shortfalls of CBR airport, because a captain chose not to land his 777 on a perfectly acceptable 2200m runway.