According to the rule that defines the ellipsis it is always represented by a sequence of three dots, or in modern fonts, by the ellipsis character, that is made of a character with the three dots in it.
Examples of the three dots sequence: ...
And the three dots character: …
(You can copy and paste the one and the other in a text editor program and change the font to a monospace font like Courier to appreciate the differences)
So by definition, and replying to the question “Is it two or three ellipsis when using it with a question mark?”:
It is one ellipsis (which is always made up of three dots).
You can find the definition in any english dictionary, for instance:
Check the section “ellipsis noun (PRINTED MARK)”.
Using your example, the correct one would be:
"So are you going to close the door...?"
Also according to The Chicago manual of Style Online; [16th ed.] 13.52 Ellipses with other punctuation
“(…), a colon, a semicolon, a question mark, or an exclamation point — may precede or follow three (but...never four) ellipsis points.(…)”
So, your eample can also be:
"So are you going to close the door? ..."