Do they run your name at the border?
Do they run your name at the border? CBP has the authority to collect passenger name record information on all travelers entering or leaving the United States.
Can the government track you with your passport?
All modern passports have chips in them, yes. Can the government track your passport? There will be records of your leaving and entering the country but your passport is not fitted with a tracking device that would enable a government to know its location or by inference your location.
What do countries see when they scan your passport?
What appears on their screen is basically all the information they have about you. All your travel history to and from that country. The consular officer's note when you were interviewed. Everything written in your passport, including identifying details and any travel history it contains.