I'm a NON US resident but I have a SSN and I formed an LLC in Wyoming. Do I have to apply for EIN or I can use my SSN? I am the only member of an LLC.
You need to register for an EIN from the IRS before you start cutting paychecks and withholding taxes for your employees. In the US there is a layer of Federal requirements on top of the state-level requirements, and this is one of those cases: there’s not going to be a Wyoming-specific EIN but instead an EIN from the IRS. See irs.gov for the online form.
[I]f the SMLLC doesn't have any employees, the business owner can use his or her social security number rather than obtain a different tax identification number.
At the same time, the article says that you must always treat the single-member LLC as its own entity, not as an alter ego. I ask, wouldn't using your SSN for the LLC violate that principle?