There are two questions here: reserving a room and staying in it. Many will say the first one is easy, you are a minor, can't enter into a contractual relationship so you can't reserve a room. That's something your parents will need to do.
However for Austria and Germany this is not exactly so as there is https://de.wikipedia.org/wiki/Taschengeldparagraph specifying how minors can do low amount transactions and so if you are 16 you can to call the relevant http://www.jugendherberge.de/ and they might reserve a bed for you (understand please the risk is much higher for them as you still can't make a binding contract but in general they will, 16 is not so young and it's just a bed for a few nights and this is why a hostel is a better choice, a hotel would risk an entire room) and when you show up with written parental consent to travel they will let you check in (http://www.jugendherberge.de/de-DE/FAQ/Jugendherbergen) finally you will need a membership from DJH which can be bought on spot.
While I can't find on their website, this page claims the Jugendherberge Köln-Deutz not only accepts cash but in fact is is cash only. Another reason to work with Jugendherberge.
As for flying, in general above 16 there are no problems as you are staying within Schengen borders so you won't even meet immigration. You need to carry written parental consent anyways which the airline might ask for. Having a passport simplifies things, you can get away with national IDs typically but a passport makes life simpler.
Have fun! Travelling alone is awesome, I started at 16 too.