Is it easy for institutions to take a week off?

It's a little long. Don't abuse the care of leaders, especially when you are just working. Unless there is something particularly important at home, it is understandable to ask 1-2 days, but asking for a week is a bit inappropriate.

Institutions have a leave system. First, as long as the procedures are complete and you are not afraid of withholding money, you can ask for leave. Second, it's not good to give people the impression that they often take time off. Of course, there is no way to get sick. Third, if you take time off, your work will cause trouble to other colleagues, and it will also cause your colleagues a bad impression on you. Fourth, there is no way to ask for leave in an emergency, only to explain clearly and others understand. Fifth, it's definitely not good to always ask for leave when there's no emergency, especially when you first go to work.