While your argument for pluralizing the first noun is logical, in practice it doesn't seem to be a unanimously accepted standard. I can find examples of each style used in different places on the web. For some publications, there seems to be no standard at all:
The most definitive answer would be from a style guide; if you're publishing something, the publisher probably has a house style guide, and I believe legal departments of organizations often have style guides as well.
Here's what the King County style guide says, for example:
No. Use as the abbreviation for number when used with a figure, in both singular and plural forms: the No. 3 choice, invoice Nos. 4311
and 5207, lot No. 23. Don't use the symbol or sign, #, to stand for
No. or number.
So it says to use the singular form "invoice" and to pluralize "Nos." It's typical that no especially compelling reasoning is given. Conformity is the main goal of this sort of organizational style guide, and logic comes second.
(There's no special reason for picking this particular guide, it was just easy to find. You don't need to follow its advice here; my point is that you should follow the advice given in your own particular style guide about this issue.)
By the way, it seems to me that there is a third option you didn't mention: "Questions Nos. 1, 2, and 3." Some people do in fact appear to take that option: "The Stone Fort And Manitoba Post Treaties Numbers 1 & 2." I also found one document that has an inconsistent use in the title versus in the text:
Change List for Revision Numbers 1 and 2:
...the changes that have been made with Revisions Numbers 1 and 2,
Of course, these are only a few examples and could easily be mistakes, but I just want to argue that this is a possibility.
In terms of logical arguments for one particular style: here's an argument for "Question Nos. 1, 2, and 3."
It's common in this kind of context to use "No. 1," "No. 2" etc. by themselves as noun phrases referring to objects rather than to actual numerals. And when they are used on their own as noun phrases, it seems logical to pluralize them when appropriate. For example, you can say "The questions were easy. Numbers 1 and 2 were multiple-choice, and numbers 3 and 4 were fill-in-the-blank."
Now suppose you want to clarify what type of objects Numbers 1 and 2 refer to. You can just add a noun adjunct before them, which will generally be in the singular, giving "Question Numbers 1 and 2." I don't know if this is the actual reasoning that led to this format, but hopefully this makes some sense.