"Do you know any bank that allows you to buy (and sell) online as a Non-resident?""
As long as you are not (USA) American, almost any LEGITIMATE bank or broker in the world will allow you (as a non-resident of their own country) to buy and sell any securities or commodities. In Singapore or Switzerland, or other offshore investment havens they normally want to see the customer in person and copy their original passport. Then there is a long many-page questionnaire to fill out It's part of the "know your customer"" rigmarole forced upon all banks in the world (who use the dollar). It is important for the bank or broker (if they want to avoid confiscation of their dollar accounts) to certify that their customer is not a "USA Person" or if they are, that they are operating through an IRS-certified agent who will ensure that their activities are duly reported & they pay appropriate USA taxes. Experience people know many legal ways to get around these rules, but it is not for me to tell anyone how to do it in a public forum. Maybe the Mentor Group here will give you guidance. (I am not part of it)... Peter Taradash