During the melting of ice, its temperature does not change. Does it change its internal energy?

Yes, the internal energy of ice changes when it melts.

And it changes in a positive direction. Simply put, it is increasing.

This effect occurs with it due to the fact that forces from outside act on the ice. Therefore, the speed of movement of particles begins to increase, due to which its internal energy itself subsequently increases.

It turns out that it is dependent on the speed of particles, which, in turn, are dependent on external factors.

In general, internal energy depends on external factors.