and can coexist in one paragraph or in one sentence, and native speakers often use them almost randomly. In general, you should not rely on them to determine how to parse a sentence.
That said, a te-form meaning "by/with ing" tends not to be in or followed by a comma. For example, and are usually more common than and even in formal documents where is preferred.
In your case, you seem to know the author (basically) prefers the style, and is not followed by a comma. So you may think this tends to mean "to teach orally" rather than "to say, and (then) teach". (Of course, it is often the case that the context or your common sense is the only clue.)