part of the answer is that a zero-beta stock must be negatively correlated with other stocks in the portfolio. So having a zero beta stock can decrease the volatility. Does that mean that the volatility a zero beta stock is lower than a risk free asset?
If we assume that the starting portfolio is well diversified, then removing a zero beta stock from it will not reduce risk, since the only risk it carries is unsystematic risk but the only risk that matters for the portfolio is market risk. Of course this is only true in the limit of perfect diversification. For a more realistic case (good but not perfect diversification) the risk reduction would be negligible.
Not necessarily. Recall the form of covariance matrix when we calculate variance of whole portfolio (to make it simple say we have two assets $\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2 w_1w_2 cov(1,2)$)
if your zero-beta stock is negatively correlated with the rest of the portfolio then of course variance is decreased since $\rho$ is negative.
However if risk free asset is substituted in, it is usually assumed to have 0 correlation with the rest of the asset, hence the overall return doesn't change (because expectation is calculated by the weight*individual stock return) but variance will increase.