Difference-in-differences in Health Economics Research

#1
Hi, I'm doing a difference-in-differences analysis of a health policy intervention.

Health clinics are paid for the percentage of eligible patients who they give the right treatment to. The clinics are measured/paid separately for each type of treatment indicator.

One year, some of the indicators stopped being paid (but others continued). I want to measure if stopping the payment had an impact on performance (relative to the control group).

I have data for every single health clinic in the country - for the intervention and control group (both pre- and after- intervention.

eg.

Intervention 2016 Intervention 2017 Control 2016 Control 2017
Clinic1 82.20% 86.14% 78.90% 78.79%
Clinic2 70.70% 68.23% 78.24% 72.46%
Clinic3 67.74% 54.22% 72.28% 64.95%
Clinic4 82.26% 87.87% 91.18% 85.39%
… … … … …
up to Clinic 450
Average 78.17% 74.14% 78.30% 75.98%

So the difference-in-differences estimator (the intervention impact) is: ((Intervention2017-Control2017)-(Intervention2016-Control2016)) = -1.97 (based on the average)

My questions are:
1. If I have data for every single health clinic (it's not a sample), should I still calculate the Standard Error and confidence intervals for the DiD estimator?
2. How best should I calculate the SE and CI for the DiD estimator? Should I use just the mean average, or can I factor in the individual pairs of measurements (for each clinic)?
3. Each clinic has varying numbers of eligible patients (I have the numerator/denominator for each); can I factor that into the estimation?
4. Can I also calculate whether there's a statistically significant change in performance variation between practices, following removal of the payment incentive? How best to calculate that?

Ideally I'd like the do the calculations on STATA.

Many thanks.