"He walked to the door, opening it to ..."
It might seem, on first perusal, to be improper because of the different tenses, but it's ALL past tense, but it allows a more dramatic delivery of the more important element of the sentence (i.e. you switch to present tense in a past tense story, because you want to set the actions apart from the rest of the sentence).
No, this is wrong. The present participle describes a state simultaneous with the main verb - in this case, implying that he's opening the door while walking to it. That's unlikely, unless he's got telekinesis or Mr. Fantastic arms or something.
"He walked to the door, wondering who had knocked," is fine. Walking to the door and wondering who had knocked are things that can happen at the same time.
Walking to the door and opening the door are sequential events, however. The opening has to happen after the walking. So it's: "He walked to the door and opened it."
"He walked to the door, opened it," and, "He walked to the door. Opened it," are both technically incorrect, but they say what they mean to say, and so are acceptable in fiction. "He walked to the door, opening it," does not say what you think it's saying. You should never use it.