Learn French: Vous n'êtes pas censés rire pendant le deuil. - You are not supposed to laugh during the mourning.

Because censé functions as an adjective and must agree with the subject. Here, the subject is Vous. The s tells us that Vous refers to a plural group (masculine or mixed). If you were speaking formally to one man, it would be censé, and for one woman, censée.

What is the difference between saying Vous n'êtes pas censés rire and Vous ne devez pas rire?

Vous ne devez pas rire uses the verb devoir and expresses a strong, direct obligation: 'You must not laugh.' Using être censé softens it to an expectation or a social rule: 'You are not supposed to laugh.' It implies that people expect you to be serious, but it is not a hard command.

Where exactly do we place the negative words ne ... pas when using être censé?

The ne ... pas always surrounds the conjugated verb, which in this case is être (n'êtes pas). The structure is: subject + ne + conjugated être + pas + censé(e)(s) + infinitive.

What does le deuil refer to exactly? Does it mean the funeral?