What are the water additives that can help accelerate the water freeze process?

I'd say no because any additive will just disrupt the hydrogen bonds between the water molecule disrupting the formation of the water lattice which forms when water freezes. This is how salt works to provent ice formation. This site as a picture of the lattice in figure 1 CliffsNotes::Biochemistry I: Water: Properties and Biomolecular Structure

This is just my own theory though I can't promise it's right!

I have heard that ice is supposed to form faster from hot water though but I don't know why.

Temple, it basically comes down to convection currents and the water evaporating so that there is less of it to freeze, so it's a bit of a cheat! It only works for certain starting conditions.
See Mpemba effect - Wikipedia, the free encyclopedia

You could add ice to the water, then it would freeze faster (bit of a cheat too, I know.):)

I think you're right temple lane, any impurities tend to lower the freezing point. Had to spread the rep :)