Answering business questions with machine learning models (scikit or statsmodels)
Why did customer service calls drop last month?

It depends on what type and features of data you have to analyze and explore the data. One of the basic things is to look at correlation between features and target variable to check if you can identify any feature that can correlate with the drop of calls. So exploring different statistic might help better to answer this question than prediction models.
Also it is always a good practice to analyze and explore the data before you even start working on prediction models as its often necessary to improve the data (scaling, removing outliers, missing data etc) depending on the prediction model you chose. 

Should we go with this promotion model or another one?

This question can be answered based on the regression or any other prediction models you designed for this data. These models would help you to predict the sales/outcome for the feature if you can provide the input features of the promotion models.
Thanks for your help on this.
This feels like a silly question, and I may be overcomplicating things.  Some background information - I just recently learned some machine learning methodologies in Python (scikit and some statsmodels), such as linear regression, logistic regression, KNN, etc. I can work the steps of prepping the data in pandas data frames and transforming categorical data to 0's and 1's.  I can also load those into a model (like, logistic regression in scikit learn).  I know how to train and test it (using CV, etc.), and some fine tuning methods (gridscore, etc.). But this is all in the scope of predicting outcomes on new data.  I mainly focused on learning on building a model to predict on new X values, and testing that model to confirm accuracy/precision.  
However, now I'm having trouble identifying and executing the steps to the OTHER kinds of questions that say, a regression model, can answer, like:
Why did customer service calls drop last month?
Should we go with this promotion model or another one?
Assuming we have all our variables/predictor sets, how would we determine those two questions using any supervised machine learning model, or just a stat model in the statsmodels package.
Hope this makes sense.  I can certainly go into more detail.