Short answer to your question:
As a U.S. resident, you can legally open a trading account with any forex broker in the world who will deal with you. And you can legally create an offshore company anywhere in the world, and do business (including forex trading) through that company from your base here in the U.S.
An offshore company is far more complex (and expensive) to set up, than simply opening an offshore trading account with one of the brokers who will deal with U.S. residents.
But, as you point out, an offshore company offers more broker choices.
As a "U.S. person" you will have tax-paying and financial-reporting responsibilities to the IRS and the Treasury Dept., regardless of how you structure your forex trading business. To the IRS, you will be responsible for taxes on your worldwide income. And to the Treasury Dept, you will be responsible for revealing all of your offshore accounts/holdings/interests, if the aggregate total of funds held in those entities exceeds certain thresholds.
But, these accounting chores are simply one of the costs of doing business legally, and keeping yourself out of trouble with the Nanny State.
I have written a lot on these subjects in this thread, as have several other members. The thread is huge (as you point out), and therefore a victim of its own success, to a certain extent. I know how difficult it can be to navigate and search this thread, especially for a newcomer. (It would be cool if the forum software automatically created an index of topics in large threads like this one, but that ain't never gonna happen.)
I will try to put together a list of links to specific posts where the legalities of this offshore broker thing are discussed, where tax issues are addressed, and where the pros and cons of opening an offshore company are batted around. May take me some time to do, so be patient.
Welcome to our "huge" thread, by the way!