And for Schengen, you'll have a stamp in and out (assuming 1 passport).

No Schengen stamps if you already live in the Schengen area. Unless there is data sharing the US gov wouldn’t be able to see it from a passport.

I suppose it will be another question on the form. Next to ‘I am not a terrorist’

As a side-note: I saw the forms that my great grandparents had to fill out when entering the US from Europe back in 1905 or thereabouts. There was a checkbox for "anarchist"

Plus ça change, plus c'est la même chose