Not sure if this helps, but in English "how did you/have you come into my room" would only be said if you were in the room when she came in (in reality you would never say this -- you would say "how did you get into my room"). On the other hand if you said "how did you get into my room" it could be said irrespective of whether or not you were in the room when she entered.
I don't think it should be wrong, so I would report that. There IS a subtle distinction in English between "How did you... something" and "How have you... something". The "have" makes a connection between a past action and the present, whereas "did" is simply something in the past.
If you find out that someone broke into your room, say a week ago, you might ask "How DID you enter my room (last week)". The action is over and done with.
If on the other hand you are in the room now, and turn around to see another person standing there, you might say "How HAVE you entered my room?" because the person's presence is having an impact on the present. (That is, the fact that a strange person has broken into your room and is standing in front of you.) However it would be equally correct (and probably even more common) to say "How DID you enter my room", because that action occurred and was completed before you noticed the other person there.
The thing is, though, that the distinction isn't really observed in Italian. The passato prossimo form used here could cover both. To my mind both answers in English should be acceptable. The chances are that whoever wrote the question was thinking of only one of the forms above, and wrote the answer accordingly.
That's either "come stai" (informal) or "come sta" (formal). They are from the verb "stare" rather than "essere". "Sei" comes from essere.
Essere means "to be". It's derivative "sei" (or è for the formal) typically mean "you are" or "are you", (depending on context), though here it means "have you". "Come sei..." = "How have you..."
Stare generally means "to stay", but it can have a broader meaning than that. When you are talking about someone's health or general well being (the above-mentioned "come stai", for example), it can mean "to be" in the sense of "a state of being". Question: "Come stai?" Answer (hopefully): "Sto bene".
Getting your head around when to use a form of essere and when to use a form of stare is one of the more problematic issues in learning Italian, but it does start to come naturally with practice.
Italian loves to use definite articles with nouns, so "my room" in English is "LA mia camera" in Italian. (Literally translated, it would be "THE my room".) "In" in this sentence functions similarly to "into" in English. When "In" and "La" combine, they become the word "nella". Take a look at heading number 3 on the Collins Dictionary page here: https://grammar.collinsdictionary.com/italian-easy-learning/using-prepositions