Upvote:1
Let's start with the easy part. The period of time you are allowed in Canada is actually 180 days, not 6 months. I never found the information on the Government of Canada website, but having been in this situation, the stamp in my passport clearly showed a date matching 180 days, not 6 months. But the border agent can write whatever date he/she wants, so check your passport to make sure. If there is no date written on the stamp, this will be 180 days after arrival.
Leaving to a non-North American country and coming back soon after will apparently "reset" your 180-day allowance. Another question kind of covered the topic, and the bottom line is that only visits to the USA and St-Pierre-et-Miquelon (a tiny island next to Newfoundland belonging to France) must fit in the 180-day allowance.
However, a border agent can always refuse you to enter the country if he/she has a strong belief you might be cheating and working illegally. It is therefore important to be able to prove you are not. Explaining your exchange and your travels, showing the plane tickets - especially the ticket to go back to Germany - will be helpful. Do not hesitate to prepare documents to prove all that, it's better to be ready than to have to argue a long time at the border.