Could you use ONE single Adsense ad for many different websites with each site being identified as a different site on an impression-per-site basis?

No, you cannot use one single AdSense ad for multiple different websites while identifying each site separately on an impression-per-site basis. google AdSense requires that each website has its own unique AdSense account or ad unit, as ads are tied to specific domains. Running ads across different sites under a single account could violate AdSense policies, leading to potential account suspension. Each site must comply with AdSense's terms of service and have its own ad implementation.