The change comes 119 years after Samoa moved in the opposite direction.
What's going to be the date? Again, from the article you could see that they will skip from December 27th to December 29th, missing the 28th. So the date will be December 29th.As to "a day isn't just some thing", a day is a 24 hour period as defined by how long it takes a planet to rotate on its axis. They aren't changing that, their days will still last 24 hours. Dates, however, are indeed just some thing, purely defined by humans, and there have been multiple different calendars over the years. See http://en.wikipedia.org/wiki/History_of_calendars
Samoa sits practically right on the International Date Line, this is the line where GMT -12 meets GMT +11, so that you are travelling forwards or back 24 hours whenever you cross over it, depending on your direction. Therefore, whichever side of the IDL they chose to base their time and date on, the time will still fit the day as we know it (i.e. dark at night). And, whichever side of the IDL they chose to base their time on, there will always be other islands very, very close to them that are 24 hours (i.e. one whole day) away from them.
Ultimately, the only difference this makes is whether their weekends coincide with those of the Americas, or those of Australasia. Since, in the past 119 years, their businesses have moved from mostly dealing with the Americas to mostly dealing with Australasia, so it makes sense to move back to being in sync with Australasia.
2) The Gregorian calendar was introduced in 1582, not "thousands of years" ago.
A day really is just a thing: I'm not any younger.
After all, it's possible to fly around the world in less than 24 hours, but you can't use that to travel forward or backwards in time, you can only ever get to a maximum of 24 hours ahead or behind of another place.
Edit: In retrospect realise that wasn't particularly helpful. I skipped an awful lot of Mondays for which the only consequence was utter joy at the two cocktail hours every other Saturday. Contrary to the great grandparent, a day really is just a thing.