I would recommend you to read [this beautiful article][1] by Racine and Li published in the Journal of Econometrics in 2004. They develop a framework to estimate regression functions nonparametrically using kernel methods, with mixed types of covariates (categorical or continuous regressors). Among other results, they show consistency of the cross-validated estimates. This is a classical article in the nonparametric econometrics literature.

The main method for choosing bandwidth parameters is, undoubtfully, the cross-validation procedure. However, other methods exist such as bootstraping (a quick google search gives: [a PhD thesis about choosing bandwidths for np kernel regression][2].

Also, if the Nadaraya-Watson estimator is indeed a np kernel estimator, this is not the case for Lowess, which is a local polynomial regression method.

Finally, the np kernel estimation of densities is extremely similar to that of the conditional mean, which is what you have in mind when you talk about 'regression'. A np kernel regression considers estimating $E(Y|X)$, where $Y$ is the dependent variable and $X$ is a (hopefully) exogenous predictor. Replacing Y by $I(Y\leq y)$ - where $I$ denotes the indicator function that equates $1$ when the event inside the brackets occurs - gives the conditional mean expression  $E(I(Y\leq y)|X)$.
Now, run a bunch of np kernel regression on $E(I(Y\leq y)|X)$ for various values of $y$. This will provide an estimate the conditional cumulative distribution of $Y$ given $X$. Now take a derivative with respect to $y$, you have a density. So what's the difference after all? Just a matter of choosing the dependent variable. The method is the same, unless you want to re-scale and impose restrictions on the CDF maybe...

  [1]: http://www.sciencedirect.com/science/article/pii/S030440760300157X
  [2]: http://d-nb.info/104355470X/34