Learn German: Wir haben den reparierten originalen Motor vorsichtig eingebaut. - We have carefully installed the repaired original engine.

When you stack multiple adjectives in front of a noun, they all take the exact same declension ending. Here, Motor is a masculine noun acting as the direct object (accusative case). Because it follows the definite article den, the adjectives use the "weak" declension. For a masculine accusative noun, that weak ending is always -en.

Is reparierten functioning as a verb or an adjective here?

It's a past participle functioning as an adjective! In German, you can take a completed action (like repariert from reparieren) and place it right in front of a noun to describe its state. When used this way, it needs an adjective ending, which is why it becomes den reparierten Motor (the repaired engine).

Why does the adverb vorsichtig come after the long object phrase instead of before it?

In German sentence structure, an adverb of manner (like vorsichtig) usually comes after a specific, known direct object. Because the direct object here (den reparierten originalen Motor) uses a definite article (den), it's highly specific, pushing the adverb closer to the end of the sentence, just before the final verb (eingebaut).

Could I use installieren instead of einbauen for "installed"?