This is what the compartment should more or less look like (pic from wiki): As you guessed, there is no changing room or something similar. A pillow and sheet like you see in the picture are provided.
There is some variation, but most people will sleep in comfortable street clothes or close to that. Usually at the end of the coach there are toilets and a washstand. The washstand is probably the closest you will get to a changing room. You can use it to clean your face, to shave, brush your teeth and eventually do a quick cat wash. No full shower. That you should get somewhere else. If you decide on the cat wash try to leave the washstand as you found it instead of flooded. There might be shower facilities in major stations (Gare d'Austerlitz in Paris has some for instance, I'm not sure about German stations).
If you expect smelly shoes/feet the best option is probably to air your feet and footwear before boarding the train. If you can carry some light sandals to replace your heavy hiking boots, that would be an option. Putting your smelly shoes in plastic bag and knotting it well closed will also make a huge difference.
Another thing to be aware of if you want to be considerate towards the other passengers (and it sounds you are, thank you) is to avoid noise for people that are already sleeping when you board the train or are still sleeping when you leave the train. If you leave very early make sure that all your luggage is easily retrievable with at minimum on noise. Postpone putting on your shoes until you are outside the compartment, in the corridor. Places to store luggage are under the lower beds (rather narrow space), above the door (surprisingly large, perfect for bulky items) and behind that little stair. Avoid putting anything behind the stair when boarding in the middle of the night because putting something there is always noisy. I often put a small bag simply next to me in the bed, but this depends largely on the size of the bag and your own size.