To what extent is the hadith "Build mosques and fill them" authentic? And must every mosque that is built be filled, or is that not a condition?

There is no hadith with this exact wording, but the command to build and maintain mosques has been mentioned in many texts; among them is the Almighty's saying: "The mosques of Allah are only to be maintained by those who believe in Allah and the Last Day and establish prayer and give zakah and do not fear except Allah. For it is expected that those will be among the [rightly] guided."