How did they end up with a 1/2 hour time difference to the neighboring countries/areas?
In the case of Newfoundland, I remember hearing that it was to make life more convenient for the fishermen. How it did that, I don’t remember. But basically, it’s just if the local government decides that they would rather be halfway between two time zones rather than in one or the other or spit in half.
Archives, man, archives.
Thanks. Afghanistan is on Cecil’s list. Not only are they off by some odd amount, they are also in the previous century as far as I can see. They executed a woman who was the victim of continuous wife beating and one of those times happened to kill her husband in defense.
A really strange time zone is Chatham Island time. It’s governed by New Zealand, 400-some miles to the NW, but it’s time is 45 minutes ahead of NZ. It’s in the Western Hemisphere, but the Int’l Date Line jogs east around it, so it’s the first land that experiences any particular date.
Being that it’s sunrise on New Year’s Day is at 5:50 and it has some relatively high mountains, people flock there to witness the first sunrise of the new year. This gathering was really big last year, and probably will be for those better at math this coming New Year’s Day. 
With regard to Australia, I think I can answer.
The areas in question are Sth Australia and the Northern Territory. The key thing here is to remember that large parts of Australia are very sparsely populated. Of the 19 million who live here, the Eastern Seaboard (Melbourne, Sydney, Brisbane and the towns in between) accounts for most of the population. Something like (90% of the population live within 100 km of the sea, mostly on the East coast.
West of this you have Adelaide, Darwin and Perth. Nowhere else has a population approaching 100 000. Since Adelaide is pretty much the only significant population centre for at least 500 kilometres in any direction, it makes sense that local time is geared to Adelaide.
Not true any more. The Line Islands in Kiribati are in time zone +14, which puts them either 15 minutes or an hour and 15 minutes ahead of Chatham Island (depending on whether it’s daylight savings time in Chatham). During the southern summer, Tonga also goes on daylight time so they are also in GMT+14 at New Years.
Because it’s much further south, on New Years Chatham has an earlier sunrise than the Line Islands.