Is #2 really illegal? What's to stop Wal-Mart from analyzing sales receipts before deciding which store-brand product to introduce next?

If it's illegal, I suspect it's only indirectly so, by some roundabout after-the-fact fair-trade-practice or antitrust analysis, based on Google's dominance of search advertising. Which means: very arguable and not much of an up-front deterrent for a motivated competitor.

In their privacy policies – which concern 'personal information' with far more legal sensitivity than aggregate ad/transactional data – Google pretty much grants themselves carte blanche to "combine the information you submit under your account with information from other Google services or third parties in order to provide you with a better experience and to improve the quality of our services" and/or "Provide, maintain, protect, and improve our services (including advertising services) and develop new services".

I doubt it, but maybe if they did explicitly use Groupon's data directly from their campaign. If they just look at searches and clicks then all that data is surely theirs to use.

Not exactly equivalent.. Wal-mart's a distribution channel, Google's more of a marketing channel. Although it gets fuzzy.

it is phony practice though it will be really hard to prove that certain decisions made by Google were based on analysis of AdWords data from Groupon campaigns.