Learn Hardcore Russian: Я точно закрыл дверь.

While точно can mean "exactly" in contexts like точно так (exactly like that), in Я точно закрыл дверь it conveys certainty—"I definitely closed the door."

Why is закрыл used instead of закрывал?

закрыл is the perfective past tense of закрыть, indicating a completed action ("I closed it and now it's closed"). закрывал is imperfective, used for ongoing or habitual actions ("I was closing the door" or "I used to close the door regularly").

Why is дверь in the accusative case?

In Russian, direct objects of transitive verbs take the accusative case. дверь is feminine, and its accusative form (the object form) happens to look the same as the nominative: дверь.

How would a female speaker say this sentence?

Russian past-tense verbs agree in gender. A male speaker uses закрыл, while a female would say закрыла: Я точно закрыла дверь.

Why is there no article like "the" or "a" before дверь?

Russian has no articles. Definiteness (the) or indefiniteness (a) is understood from context. Here it's clear from the situation that it's "the door."