Can a child spread chicken pox by playing on a water slide with other children at a party?

Yes. The rule is that if all of the chicken pox blisters have dried up and formed scabs then they are no longer contagious. Children who are 4 to 5 years old or older should have received two chicken pox shots. In which case they should be immune. If there is an unvaccinated child at the party they would be at risk.
Yes. Chickenpox can be spread through the respiratory tract as well as by direct contact with the lesions once they appear, and playing together during a party presents many ways of transmission during any phase of the illness.