We present cross sections for rotational, vibrational, and fine-structure transitions in He-CaH((2)Sigma) collisions at cold and ultracold temperatures calculated using the ab initio potential energy surface reported in the preceding paper. Rotational quenching is fast, vibrational quenching is slow. The spin-rotational interaction, although small and having no influence at temperatures above 10 K, changes significantly the rate coefficients for rotational quenching at lower temperatures. The theoretical rotational, vibrational, and elastic cross sections are compared with the results of a buffer gas cooling experiment carried out at a temperature of about 0.4 K. The theoretical predictions for the vibrational and elastic cross sections are larger than the measured values. The sensitivity to the potential energy surface is explored. A modified surface diminishes but does not remove the differences between theory and experiment. (C) 2003 American Institute of Physics.