Use of series inductor to control small 120v blower
Q1 Would it be best to use a buck xfmr instead?

If the blower is running the way you like with a series inductor, there is no need to change that. It is a wash whether the transformer would be more or less efficient. One disadvantage of the inductor method is that it affects power factor, as you are aware. Did didn't specify the power of your blower, but my guess is that it is relatively small, and power factor for such a device is only an issue if you want to make it one.

Q2 How does the inductor method affect cost of operation?

I don't know how the power utility bills in your location. Where I live, they charge based upon real or true power, not apparent power. This means that people can actually run their meters in reverse by supplying power to the grid. Your true power will be approximately the same whether you use an inductor or transformer.

Q3 I note that the motor runs cooler either way. What is happening regarding phase shift, like EIcos theta?

The inductor is forming a voltage divider with your blower, and current is, in all likelihood, out of phase with your line voltage. Most motors tend to be inductive loads on their own, so how much your inductor has influenced the pf is hard to say.