If you’re not a US citizen but you’re traveling in the US and you own a US company and you occasionally do a couple hours of work for customers (emails, , but mostly sales are automatic) do you really need to get immigration work permit paperwork like an E3 or something to legally be doing that or is it OK?
It depends on exactly what you do when here but if it's work, then yes, strictly speaking, you need work authorization. (Years ago, this wasn't true and one could travel to the U.S. as a business visitor to conduct business on a limited basis if employed by an entity abroad.) The problem is that such a work visa (the E-3, for example) requires a company in the U.S. to act as the petitioner/employer.