Should the observation window include the same dates for all the users? I'm building a churn model that is trained on  users' historic data(observation window).
For this example, let's say that I want to train the model on the last week of use of each user.
Is it fine that the weeks of each window will be different according to the last week of use for each user? For example the next figure:

Are there are any advantages if the observation window starts and ends on the same dates for all the users?

This is quite fine. A typical time series method also looks back a few days/periods at different time instants. You just need to make sure the dates you use are not inside the test period, for any user. A disadvantage of using a single day/date for training purposes is that the data may fall into a very specific period of time and learn features specific to that time interval, e.g. holiday period. For this reason, it doesn't allow you to utilize time-based features.
