If you responded: "I am asking that you open the door" and it wasn't correct, you can use a red button at the bottom left of the screen to report "my answer should be accepted". They are very good about adding correct answers to the list. Same with, "I'm asking that you open door" is a fine translation, in my opinion.
Not really. There's no reason to inject "please" into your translation. Mi petas can mean "I request" or "please" - but not both at the same time.
Side note - I once, about a year into my Esperanto studies, used the expression "Mi petas akvon" - with the intent of meaning "water please" or "I kindly ask for water." My host misunderstood me and asked me if I was taught by a Hungarian Esperantist. I found out later (I think it was among Hungarian Esperantists in Croatia) that a fairly common mistake among Hungarian Esperantists is to say "Mi petas" in place of "I would like". I remember one particular person saying repeatedly "cxu vi petas akvon"... if that should ever happen, just roll with it and say "jes, mi petas" ... unless of course you don't actually want water - in which case say, "dankon, ne."