US banking regulations don't apply to these dollars? Well, of course, because US banking regulation only apply in the banks in the US. Banks that are located outside of the US are subject to whatever regulation is in place in the location that they're at. Does that mean that Eurodollars are unregulated? No, it doesn't.

Second, currencies don't have interest rates. Only debt instruments do. I have no idea what you're talking about when you say that Eurodollars and US dollars have different interest rates.