The correct answers are Before I left for the airport, I packed my swimsuit, sunscreen, and sunglasses. and I grabbed my passport, locked the door, and ran to the taxi.

Use commas to separate three or more items in a series. The comma before the "and" (the Oxford comma) is generally preferred for clarity. Also, use a comma after a dependent clause that starts a sentence.

When I finally arrived at the gate I realized I forgot my ticket. is missing the comma after the introductory clause ("...gate, I realized...").

My suitcase was full of shirts, pants and, shoes. has a misplaced comma; it should go before the "and", not after it.