Is it permissible to pray in small mosques that have defied the decision to close them? And is it better to pray Fajr at home or in the small mosques that delay the Iqamah?

It is necessary to comply with the state's orders to close small mosques if that achieves the protection of people from illness, as long as it serves the public interest, and it is permissible. Jurists have stipulated the obligation to obey what the Imam commands when it serves a public interest, both outwardly and inwardly. As for the timing of Fajr prayer, it should not be prayed until after verifying the entry of its time or having a strong presumption thereof. If trustworthy scholars have issued a fatwa that the adhan time is before the entry of Fajr, then do not rely on that calendar and pray Fajr after its time has entered. And if they have issued a fatwa that the timing is correct, then what others say holds no weight.