Just an addition about the issues regarding hotel bookings. It is not directly required by law in Germany to be over the age of 18 to book a hotel room, but there are so many legal grey areas and pit-falls to consider, that most hotels don't allow persons under 18 to book a room or even use a room alone, if they are travelling alone without a parent or guardian. You are also usually excluded from all online booking services like booking.com, Expedia or AirBnB. It is not necessarily sufficient that your parents book the room for you, you may still not be allowed to stay alone.
- One issue is, as jpatokal already mentioned in a comment, that you only within very restricted limits are allowed to enter a contract, which a hotel room booking legally is. If a hotel allows you to book a room on your own, even if you paid cash in advance, your parents can to a certain extent dispute this contract later and demand it annuled with the consequence that the hotel will have to return any payment already made.
- A further issue is, that even if the hotel allows you to stay, they are not allowed to grant you any form of credit. This is an issue if the hotel has accessible mini-bars or offer room-service or meals chargeable 'on the room' with payment when checking out. In theory, you could empty the mini bar and feed graciously during your stay just to deny payment when checking out, since the hotel was not allowed to let you eat on credit in the first place. Most hotels rightfully tries to avoid this situation at all.
- Even alcohol access regulation may be an issue. If the room only has rooms with a mini-bar and the mini-bar is stocked with strong spirits, they will therefore not be allowed to let you stay there alone.
All youth hostels associated with DJH (the German Youth Hostel Association) do however let guests between 14 and 17 stay alone if they have parental consent. Strictly speaking, they require you to bring a written consent declaration from your parents. I am not sure how strictly they check if you have a consent form, but it wouldn't hurt to bring one. The form seems to only be available in German, but just run it through an online translator and you will find out what to enter where. It is quite straight forward. Be aware though, that there are also plenty of hostels or youth hostels, which are not associated with DJH. These may have their own rules and may or may not allow you to stay alone.