We completed a new survey for H I emission for a large, well-defined sample of 154 nearby (z < 0.1) galaxies with type 1 AGNs. We make use of the extensive database presented in a companion paper to perform a comprehensive appraisal of the cold gas content in active galaxies and to seek new strategies to investigate the global properties of the host galaxies and their relationship to their central black holes (BHs). We show that the BH mass obeys a strong, roughly linear relation with the host galaxys dynamical mass. BH mass follows a looser, though still highly significant, correlation with the maximum rotation velocity of the galaxy, as expected from the known scaling between rotation velocity and central velocity dispersion. Neither of these H I-based correlations is as tight as the more familiar relations between BH mass and bulge luminosity or velocity dispersion, but they offer the advantage of being insensitive to the glare of the nucleus and therefore are promising new tools for probing the host galaxies of both nearby and distant AGNs. We present evidence for substantial ongoing BH growth in the most actively accreting AGNs. In these nearby systems, BH growth appears to be delayed with respect to the assembly of the host galaxy but otherwise has left no detectable perturbation to its mass-to-light ratio or its global gas content. The host galaxies of type 1 AGNs, including those luminous enough to qualify as quasars, are generally gas-rich systems, possessing a cold interstellar medium reservoir at least as abundant as that in inactive galaxies of the same morphological type. This calls into question current implementations of AGN feedback in models of galaxy formation that predict strong cold gas depletion in unobscured AGNs. (Abridged)
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