Learn Russian: Мальчик дрожал от страха.

The preposition от is used for involuntary physical or emotional causes. Since shivering is a physical reaction you can't easily control, and fear is an emotion rather than a conscious motive, от is the perfect choice. You would use из for a conscious, deliberate choice, like doing something out of curiosity (из любопытства).

Why does страх change to страха in this sentence?

The prepositions от and из both require the Genitive case. Since страх (fear) is a masculine noun ending in a consonant, we add -а to form its Genitive, making it страха.

Why is the verb дрожал imperfective?

The imperfective aspect is used because shivering is an ongoing process or state. The sentence focuses on the boy being in the middle of shivering, rather than a single completed action.

Could I use из-за (because of) instead of от here?

You could technically say из-за страха (because of fear), but от страха sounds much more natural in Russian for direct, involuntary physical reactions to feelings or environment, just like shivering from cold (от холода) or crying from pain (от боли).