Does the amount of food coloring affect the speed of ice melting?

Yes! The food colouring is acting as an impurity in the ice. When an impurity is present in a solid, it causes a decrease of the melting point. When an impurity is present in a liquid, it causes an increase in the boiling point. So, pure ice melts at 0 degrees celcius. When the impurity is present, it may melt at probably -10 degrees celcius (I'm just saying!). So, it would take more time to melt. And when there is more food colouring (more impurities), it would definitely cause the melting point to decrease and thus, take longer to melt.

* I hope that helps!