"Please open the door."
Translation:Bonvolu malfermi la pordon.
The imperative is the verb mood you use when, for example, giving someone instructions. In English, it takes the form of the bare infinitive: "Be good."
Also, after the imperative in Esperanto, you must use the infinitive. So your sentence should be "Bonvolu verŝi*".
Saying both "bonvolu" and "mi petas" is a little redundant since they both mean essentially the same thing, but that's style, not grammar.
And since "verŝi" is generally a transitive verb, you'll probably need to include a direct object, which takes the accusative declension, which is the suffix -n. "Bonvolu, verŝi gxin, mi petas."
*(or versxi if you can't make the letters with the diacritical marks)
The country name Portugal comes from the Latin pordus, which means "harbor/port". "Port" as in "harbor" and the Spanish/Italian/French/etc. word that means "door" go back to the same Proto-Indo-European root. So it's not a coincidence.