There is no evidence to suggest that it is haram to eat duck or pigeons, so we go back to the original principle, which is that they are permissible.

If we assume that the carmine is derived from female ants and the sweet is not harmful, then there is nothing wrong with eating it.

It is not permissible for Muslims to eat balut eggs because it comes under the heading of eating Maytah (something that has died without being slaughtered properly), and eating Maytah is definitely prohibited according to Islam.