Burning a transformer and replacing it from 110V to 220V
Yes, it might be damaged because as there was double the voltage into the transformer, there was double the voltage out from the transformer too.

With a transformer that has identical output rating but has 240V 50Hz input. Note that the transformer rating reads on the label: 8 Watts, 9 Volts. Just as a disclaimer: if you don't know how to work with mains voltage circuits safely, leave the modifying to a competent service technician.