Is a no trespass order from Walmart legally binding?
The answer to all three questions is potentially yes. There are are far too many variations across the 50 US states as to what is required to make a trespass order legally binding, but in many states, simply being ordered not to return to private property is sufficient, even if made orally. And if the order is valid, your returning without permission could absolutely be criminal and lead to your arrest. It would be foolish to return to Walmart and just see what happens: if you'd like to return, you should probably clear that with the company beforehand.