If I was a TV host of a TV show (similar to The big Brother)and wanted to talk about the events happened during the week to the participants, considering that they first entered the house on Monday, could I consider the week the one that started on Tuesday and ended on Monday? And so would it be acceptable to say" This week a lot has happened, for example every night while you were sleeping one of your belongings has been taken away and hidden and your task is to find them again in the house"?
Terms such as this week or next week are inherently vague, and they could mean different things depending on the context. Not every week needs to start on a Sunday or Monday.
Some people (such as police officers, firefighters, nurses, and convenience store clerks) may not work a Monday through Friday duty week. For them, a work week may start on a Wednesday, and their "weekend" may therefore start on a Monday.
Your example is another good example. If a reality television show airs on Tuesday night, and the host of the show says, "Let's recap what has happened this week," I would assume that the "week" being discussed started at the end of the last show, no matter which day that happened to fall on. (Incidentally, chances are the show was pre-recorded anyway, so, for all we know, what was heard by me on a Tuesday may well have been originally uttered on a Thursday).