Learn French: Tu es censé respecter la ponctualité. - You are supposed to respect punctuality.

Yes, it does. Because it acts as an adjective here, censé must agree in gender and number with the subject Tu. If you are talking to a woman, you must add an 'e' and write Tu es censée. In spoken French, however, they sound exactly the same.

I've seen the word sensé spelled with an 's'. Is that the same word?

No, they are homophones (they sound the same) but have completely different meanings. Censé (with a 'c') means 'supposed to,' as in this sentence. Sensé (with an 's') means 'sensible' or 'logical' (like une idée sensée). A good trick to remember: censé is almost always followed by an infinitive verb like respecter, whereas sensé usually stands alone to describe a noun.

Does être censé only express rules and obligations?

It primarily expresses an expectation or a theoretical obligation, similar to 'meant to' or 'supposed to' in English. However, just like in English, it can also express a widely held belief or rumor, such as Il est censé être riche (He is supposed to be rich). In this sentence, it clearly expresses an expected behavior.

Is respecter la ponctualité the most natural way to tell someone to be on time?