Is it true what was said about the people of Madinah receiving the Messenger of Allah, peace and blessings be upon him, with the song "Tala' al-Badru 'Alayna" (The Full Moon Rose Upon Us), and does that permit songs if they aim for the nation's advancement?

Singing is not absolutely forbidden; rather, there is a detailed explanation concerning it. Applying the term "singing" to an anthem is permissible. Singing is the beautification of the voice with metered words or the recitation of poetry with melodies, and "taghannī" (singing/chanting) is trilling. The caller to Islam should clarify to people that some of it is forbidden and some is permissible.