While I'm not a Germany specialist, the reunification issue is something I've looked at because it's the most relevant example that academics and policymakers studying the potential reunification of North and South Korea use. Hopefully someone with more background can answer this more usefully, but I can touch on a few very general points.

"How great was the financial burden on West Germany after reunification with the East?" The short answer is that the financial burden was and remains staggering.

The slightly longer but not-as-good-as-I'd-like-it-to-be answer: The general academic consensus is that reunification costs have been roughly $1 trillion per decade since 1990. If the IWH figures cited in that article are ballpark (and it was a report commissioned by the German government because even they don't know exactly how much they're spending!), that's like saying that half of Germany's total economic output in a given year has been spent on the last few decades.

This actually predates the reunification. The West German government actually took over some of the financial responsibilities of its East German counterpart beginning in 1989, such as pension payments and other social spending, and these were paid in expensive West German deutschemarks rather than the weak East German mark. I think it was P.J. O'Rourke who once referred to the East German mark as a "horse tranquilizer" on the world financial market, and it was a pithy way of expressing an unfortunate truth about the buying power of even the wealthiest Soviet satellite state.

Unfortunately, I don't know the particulars of what happened to specific industries or job prospects while the governments knitted the German regions together, but I do know that the reunified Germany entered a period of economic malaise in the 1990s and early 2000s. This is where things start to get murky and economists still question how many problems can be attributed to the ongoing pain of reunifying the countries (constructing or reconstructing infrastructure in East Germany that didn't wind up stimulating the economy, subsidies paid to poorer municipal governments in the east, unemployment benefits for the East where unemployment is consistently about double the rate in the west, etc.) and how many would have happened regardless due to the high cost of German labor and increased competition from manufacturers elsewhere.

The reason that this scares the shit of Korea specialists is that East Germany's economy was consistently about half the size of West Germany's from the 1960s onward. They were poor in comparison to the developed world, but not that poor, and East Germans usually had access to some Western media and products. North Korea's economy is roughly 1/18th the size of South Korea's at present, so ... yeah.

"When did Germany finally pay off the costs of reunification?" The German government would love to know the answer to this. It hasn't happened yet and will probably not happen for the forseeable future.

There are still a number of very noticeable political and economic divisions between the two regions and almost none of them are in the east's favor. These range from things important enough to merit academic and economic attention, such as long-standing migration patterns from East to West Germany for jobs and fights over how East German history will be taught to the next generation, to things that academics usually don't think about much at all.

I'll give you an example of something that academics usually don't study but will nonetheless be painfully obvious to most Germans. The German Bundesliga, or national football (soccer) league, is among the best leagues in the world, but there are basically zero former East German teams that can compete in the first tier of play. This is a map of the teams competing in the 2013-2014 Bundesliga and any 20th century historian will notice immediately that its participants (with the exception of Berlin's Hertha BSC) stop short of the Cold War border. There was even a huge controversy over whether Berliner FC Dynamo (the Stasi's preferred club, and long dogged by allegations that matches were thrown for their benefit) had the right to display a star on its uniforms in recognition of its old East German championship titles. The book Soccer Against the Enemy actually has a fascinating look at the old East German league and about what happens when a win can be considered a political (rather than athletic) victory.

I hope that helps at least a little, but I do hope a Germany specialist around here can chime in with more detail.\

EDIT: I just remembered a comment I left once on the impact of the euro on Germany's export sector, and why economic weakness elsewhere in the eurozone has actually helped Germany's finances and thus the continuing costs of reunification.

This was a pretty thought-provoking editorial in Der Spiegel asking if Europe might have weathered this better if the two Germanies had never unified, and it again raises the specter of what The New York Times article linked above is discussing: Why Germany has seemed stubbornly resistant to continued bailouts of weaker European economies. At this point the Germans have thrown about $2 trillion at their own problem that won't be going away for a very long time, and they have soured on the idea of correcting systematic economic weakness with money.

As William Faulkner once wrote, "The past is never dead. It's not even past."

cost of reunification is estimated between 0,95 bis 1,6 trillion Euro (Billion in German is 10^12 = trillion), a big part for this is social expenses like financing of pension funds - and unemployment benefits as East German industry was destroyed/dismantled.

http://de.wikipedia.org/wiki/Kosten_der_deutschen_Einheit

By 1989 the GDR was essentially bankrupt, foreign debt was around the equivalent of 172 billion euro; upon unification savings of east german citizens were exchanged 2:1, however on the market the exchange rate was 20:1

http://www.staatsverschuldung.de/ddr.htm

I guess payments for unification will go on forever (see compound interest); well, maybe not forever: Germany finally did pay off WWI reparations in 2010

http://www.welt.de/wirtschaft/article9923669/Deutschlands-Reparationszahlungen-laufen-aus.html

I'm not sure if this is within the scope of your question, but in terms of ramifications the German reunification had a large impact not only on the economy of West Germany but also on the economies of many other nations in Europe.

At the time most nations in the European Union had fixed their interest rate to the one used by West Germany through the European Monetary System. But as a result of reunification Germany began experiencing a lot of added economical activity. Fearing that this increase in economic activity would be too strong the German Bundesbank (central bank) raised interest rates, forcing the other EMS nations to follow suit even though they were not experiencing the same increase in economic activity.

Economic output in other EMS nations suffered as a result having too high interest rates (as well as uncertainty about whether they would stick with EMS or not) and the average unemployment in the EU rose from 8.7% in 1990 to 10.3% in 1992. An economist-focused subreddit might be able to provide you with more in-depth answers to your questions though.

Source: Page 154-155 of Macroeconomics - A European Perspective by Blanchard, Amighimi and Giavazzi, FT Prentice Hall, 2nd edition, 2013.