The ESTA replaces the paper form that 'visa-waiver' passengers used to fill out on the flight. I do not believe the US has an agreement with the UK, any other EU nation (which would be contrary to EU data privacy law anyway), or any other third country for exchange of information to verify ESTA data. The US does have an agreement with the EU on sharing PNR (Passenger Name Record) data - but this data does not include the data the US is seeking.
My goodness, how would anyone else interpret 'Moral Turpitude'.
ETA is similar I believe, they rely on you to be honest.