I'm a reasonably wealthy merchant in 1550 Germany and I want to send a message to another merchant in Constantinople/Istanbul. How do I do so, and how much would it cost?

There was no organized system of mail between those two locations so unless you wanted to go yourself you would have to find someone who was willing to personally deliver the message for you. If you were a merchant who knew a merchant in Istanbul, possibly you would already have contacts who did business there and you could ask them to deliver the message for you or have it delivered for you when they next sent a ship there (or knew someone who was sending a ship there, etc.). Depending on how well this contact knew you and how much of an inconvenience delivering the message was would determine the price, but if they were already traveling to the city for other business then they probably wouldn't ask very much. If for some reason you didn't have any trusted contacts with Istanbul but you still really wanted to deliver a message to this other merchant there (or perhaps it was a really secret message that you couldn't risk anyone else getting ahold of), then you could also specially pay someone to act as a messenger/and or business representative. They would then probably gain passage on a ship to Istanbul (probably departing from the Low Countries or a Mediterranean port like Venice or Marseille) and deliver it themselves. That could be very expensive since becoming a passenger on a ship wasn't cheap and you'd have to pay someone for a lot of time since the journey could take several months each way and pose a lot of risks.