Learn Italian: Il rumore lo ha spaventato molto. - The noise frightened him a lot.

Actually, no! This sentence is included as a great reminder of the standard use of lo. Here, lo is a direct object pronoun simply meaning him (or a masculine it, like an animal). It is important to distinguish between lo replacing a specific noun and the pro-clausal lo which replaces an entire statement or concept.

Is it more common to write lo ha spaventato or l'ha spaventato?

Both are grammatically correct, but l'ha spaventato is much more common in everyday spoken and written Italian. The pronouns lo and la usually drop their vowel and combine with an apostrophe before forms of avere that begin with h or a vowel.

If the sentence was about a woman (The noise frightened her), how would it change?

It would become Il rumore l'ha spaventata. Remember that in compound tenses like the passato prossimo, whenever you use a third-person direct object pronoun (lo, la, li, le) before the verb, the past participle must change its ending to agree with that pronoun in gender and number.

Could I use the phrase avere paura instead of the verb spaventare to express this?