I think there are a number of things to consider.
Showers: I believe those are not deluxe sleepers, i.e., they do NOT have showers in the compartment. The showers would be at the end of the car and shared with everyone. Some train stations might have shower facilities (I know Munich does).
Luggage storage: I don't think that is one single train for the whole week. Rather it is a series of different trains. Hopefully all the stations will have luggage storage facilities.
Note, you can set up the schedule with any number of extra days in each city, so you could take the train one night and then have a hotel the next. That might somewhat solve the above questions.
You can only book the 7-days nights package by phone, so maybe you can get some of the questions answered. I would be good to make sure you can get adjoining 2 person compartments since the sleepers are for 2 or 3 people, only.