Learn Croatian: Otključao sam vrata pa sam upalio svjetlo. - I unlocked the door, and then turned on the light.

The conjunction pa specifically shows a sequence of events, meaning "and then" or "so". First you unlocked the door, and then you turned on the light. If you used i, it would simply list the two actions without strongly emphasizing the order they happened in.

Is vrata (door) a feminine singular word because it ends in -a?

No, vrata is actually a neuter plural word. In Croatian, "door" is a word that only exists in the plural form (like "scissors" or "pants" in English). Because it is neuter plural, its accusative form (used here as the object) ends in -a, just like its dictionary form.

Why do we repeat the helping verb sam before upalio?

When connecting two past tense actions with pa, it is very common and natural to repeat the helping verb (sam) to make two complete clauses. You could theoretically drop the second sam, but keeping it makes the sequence of events feel clearer and more balanced.

Why does the verb upalio have a masculine ending if svjetlo (light) is neuter?

The past tense verb always matches the subject (the person doing the action), not the object. The hidden subject here is ja (I), and because the speaker is male, he uses the masculine endings for both otključao and upalio. The word svjetlo is just the object receiving the action, so it doesn't change how the verb is spelled.