New passport, old one not expired

This is an absolutely normal thing to do, for exactly the reason you did it. You have nothing to worry about. Good luck with your interview and your studies.

While I haven't been able to verify your info about the validity of the passport, I don't think you have to worry. According to this site, the passport has to be valid for three months upon arrival. On the other hand, they suggest that the passport be valid for the duration of the course.

As ajd already mentioned, people frequently apply for a new passport before the old one expires, mostly to get the new passport before the old one expires (regular processing time in Germany is 4-6 weeks, just to give you some numbers), or because they changed their name, because the pages are full, because they don't resemble their picture any more, ...

I don't think you will be asked about the renewal, but if they ask, don't overexplain. A simple "I wanted the passport to be valid for the entire duration so I don't have to worry about it" sounds like a perfectly valid reason to me.

The old one is cancelled, so expiration date and all the data in there has no more meaning.

But if you wrote somewhere in the form the number of your old passport, it is better to have with you also the cancelled one. It will speed up things: it shows up that you control both passports (so no identity theft), and that both passport are for the same person (especially if you have a common name, this could slow down things).