Michal,
To move a whole week in your TrainingPeaks calendar, hover your cursor over the vertical three dots menu to the right of all of your weekdays. It should say “Week Controls”. You’ll see options to cut, copy, paste and more. From a workflow perspective, if you are intending to repeat a week and need to move everything forward, I suggest starting with the last programmed week – moving that week to a future week and then repeat the process working your way back to the present. If you start working from the current week to the future, it will get very confusing with workouts on top of each other.
For specific questions about your TrainingPeaks calendar, check the Help Center on the TrainingPeaks website. The webapp is always getting updates, and you’ll generally find the most current information in the Help Center.