"It's just the wind, Marsha. Nothing to worry about."
открыва́ть - Imperfective
открыть - Perfective
The hint on, "открываю," states that it means, "Do I open?" Does that mean the word alone can be used as a question?
No. The hint shows that "Я открываю", if used as a question, means "Do I open".
Why is дверь in the nominative case?
It's not in the nominative - it's accusative because it's the direct object. Feminine nouns ending in ь don't change for accusative.
Here's a table of noun-ending declensions showing this: