Taken statewide, the census data is just a constant and 1) can be done with FREQ. You can test the proportions against a hypothetical distribution (like uniform). If you have populaiton by year, you will get a more precise estimate.
Ditto 2). You will need to know when the new procedure started.
To look at 3) , I would use LOGISTIC regression; it does not require the Census data. You could use year as a continuous predictor. Then the type of procedure could be another binary predictor.
You may not have enough sample size to estimate hospital effect, let alone provider effect, in 3.