Learn Spanish (Latin America): El sarcasmo requiere mucho ingenio para no ofender al público. - Sarcasm requires a lot of wit to not offend the audience.

In Spanish, when you talk about an abstract concept or a general category (like sarcasm, love, or science) as the subject of a sentence, you almost always need to include the definite article (el or la). While English just uses "Sarcasm", Spanish requires El sarcasmo.

Since this lesson is about todo un, could I say requiere todo un ingenio to mean "requires a complete wit"?

Not quite, and the reason comes down to countable versus uncountable nouns. Todo un is used with countable nouns to emphasize a trait, like todo un genio (a true genius). Ingenio (wit or ingenuity) is being treated as an uncountable concept here, so it naturally pairs with mucho (a lot of) rather than todo un.

Why do we use the infinitive ofender after para no instead of using the subjunctive?

We use the infinitive after para because there is no change of subject. The sentence expresses a general statement where the entity needing the wit is the same one avoiding the offense. If we introduced a new subject (like "so that the audience doesn't get offended"), we would need para que plus the subjunctive: para que el público no se ofenda.

Why is there an al before público?