1. Adverbial clause is used as an adverb to modify a verb, an adjective, or an adverb.
2. An infinitive is a verb form that usually starts with "to.": to talk; to like etc.
3. <em>"to show us the cave paintings"</em> is an infinitive phrase. <em>The other "to" in "to</em> <em>the ceiling" is a preposition.</em>
4. "now here's your kettles, done" is a vernacular because it contains informal language: here's your kettles (<em>plural word </em><em>and</em><em> a singular verb</em>); done (instead of <em>it's done</em>.)