The emphatic "To do" and something else

I always have seen the verb to do like auxiliary to make questions or negations
But it’s the first time I see it like auxiliary to get emphasis
There are three ways as long as I know (que yo sepa)

One: to insist about you say, for example:
-She does look pretty.

Two: to contradict another person says, for example
-He didn’t come
-He did, but he didn’t stay long time

Three: To order to another person, for example:
Do sit down, please.

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today I heard a think attract my attention
here you are
one million
two million
three million
...
thousand million
...
million has not plural like in Spanish
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The Spanish have twenty "dedos"
English people have ten toes (at feet), eight fingers (at hands) and the two thumbs (los gordos)
the canarian have ten "dedos" at hands and ten "ñoños" at feet.