Thanks for the memory aid.

Porta is door, cancello is gate

'open' is fine. it's an adjective

You would use "opened" as a past participle, as in "He had opened the door."

"The door is still open." = «La porta è ancora aperta.»

"aprire" is the infinitive form of the verb => "to open" , in English.

"apre" is the 3rd person singular conjugation of the present tense indicative form of "aprire" => he opens, she opens, it opens.

io apro, tu apri, lui/lei apre, noi apriamo, voi aprite, loro aprono

"aperto/aperta/aperti/aperte" are adjectives and have to match what they are describing in gender and number.
Il porto è aperto. The door is open.
I porti sono aperti. The doors are open.
La scatola è aperta. The box is open.
Le scatole sono aperte. The boxes are open.

la porta = the door (as well as a few other meanings: http://www.wordreference.com/iten/porta)

l porto = the port or harbor (as well as a few other meanings: http://www.wordreference.com/iten/porto)