Learn French: Le savoir-vivre exige une tenue formelle.

To express this as an expectation of behavior, you could say: On est censé porter une tenue formelle (One is supposed to wear formal attire). Because être censé must be followed by an infinitive, we have to introduce an action verb like porter (to wear) or mettre (to put on) rather than just translating the sentence word-for-word.

Le savoir-vivre literally translates to "knowing how to live." Does it take an -s if used in the plural?

No, it is invariable. Because it is a compound noun formed by combining two infinitive verbs (savoir and vivre), it never takes an -s. If you ever needed to make it plural, it would simply be les savoir-vivre, though it is almost always used in the singular to mean "manners" or "etiquette."

Could I use demande instead of exige here?

You could, but exige (from exiger) is much stronger and more natural for this context. While demander simply means "to ask," exiger means "to demand" or "to strictly require." When talking about the strict rules of etiquette, exige captures that non-negotiable expectation.

I know French has many false friends. Does formelle exactly match the English "formal" here?