So how does a cheap currency benefit Germany according to this theory?
Another thing is that if production costs go down (although you don't say why they're going down, it seems a random assumption on your part), then competition among exporters will drive the price of exports down. I mean, this is Economics 101.
So, this only works if a large part of the cost is labor (this is the model china used in the last few decades) in which case the cost of production definitely goes down. I'm no expert in Germany's economy, maybe they have more materials / energy cost that they need to pay for in their home currency?
Your analysis is incorrect. Markup is a function of market power. If market power remains the same, an increase in markup cannot last for long. Competition will drive prices down until markup goes back to its previous level. Therefore the end result is a fall in the price of exports. Whereas for importers the opposite is true, imports become more expensive for local purchasers. This is what is meant by "selling cheap and buying expensive", which is exactly what happens when a currency depreciates.
Another thing is that if production costs go down (although you don't say why they're going down, it seems a random assumption on your part), then competition among exporters will drive the price of exports down. I mean, this is Economics 101.