Some government sites or real estate sites like zillow, provide a parcel number for houses which seems to be a unique identifier for that house; is there a site where I can find a list of all parcel numbers in US?
Assessors Parcel numbers in the US are assigned within specific jurisdictions (usually counties, which are smaller than states and often larger than cities or towns). Within a single jurisdiction they will have a consistent format and be unique, but across multiple jurisdictions you have no such guarantee and will likely see a fair amount of variance in formatting (see, for example, the different formats used by Fresno County, Warren County Missouri, and Clark County Nevada).
To my knowledge there is no single source of parcel data across the entire country, you will mostly have to look up the particular jurisdiction you're interested in, but there is a significant amount of federated parcel data on data.gov provided by cities, states, and counties.
You may have more luck identifying individual properties by geocoding street addresses and using census data -- but both of these have their limits depending on the granularity and quality of data available.
Open Addresses focuses on street centerlines data, but they are collecting parcels data as well. I'm not 100% who to contact or where the parcels data is being collected, but would be worth your time to reach out to them and get access to what they have.