How do I determine if a Google Play app requires Google Play Services? Or does every app listed on Google Play require it?
You can use Yalp Store for this. It is a libre app which et al list trackers, shows ads and whether the app uses Google Play Services or not.
If an app requires Google Play Services, then as soon as you open the app, you will be warned that you can't run the app unless you have Google Play Services or in better cases, that you will have limited functionality or that you may encounter unintended behaviour. Not all Google Play apps require Google Play Services.