I don't understand why the course is divided into Week 1, Week 2, etc.
Since the moment I started the course, is there a deadline for completing the assignments and watching the lectures?
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The only deadline is 31 Dec 2014 if you are going for a certificate. There are Weeks because you are doing the same course as the "in person" Harvard students who took CS50 on campus, and for them, those were the actual weeks of the term.
On the course's edx page, they have a suggested schedule (that updates automatically) to give you some "soft" deadlines to keep you on track if you have just started: https://x.cs50.net/2014/schedule