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What obligations does the company have to meet federal tax obligations? - Your company itself does not have any U.S. federal income tax obligations. It will be considered a "disregarded entity seperate from it's owner" under U.S. federal income tax principles. http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Single-Member-Limited-Liability-Companies That is assuming you have not made an entity classification election via Form 8832 to elect corporate classification.
If a single-member LLC does not elect to be treated as a corporation, the LLC is a "disregarded entity," and the LLC's activities should be reflected on its owner's federal tax return. If the owner is an individual, the activities of the LLC will generally be reflected on:
Generally if your only source of U.S. income is from investment trading (as mentioned) above you would not have any U.S. source income and not have a federal tax return filing requirement. Note that under IRC 864(b)(2) there is a safe harbor for foreign people investing in the U.S. - this basically states that if you only use a U.S. broker and trade in securities it will not be considered a U.S. trade or business and the source of the income will be your personal domicile.
I do not see any U.S. federal income tax filing requirements for your personal self simply due to the trading activity. You should review Form 1040NR instructions here to determine if you have any other income subject to U.S. taxation: www.irs.gov/pub/irs-pdf/i1040nr.pdf
When do any LLC tax returns need to be filled and how are they returned?-as mentioned above there is no LLC federal tax return, it would be your individual return (Form 1040NR)(assuming you are not a U.S. citizen). The due date for this return is the generally April 15th (maybe 16 or 17th depending if the 15th falls on a weekend) and can be extended via Form 4868 till October 15th.
Also, are any other documents required to be submitted to the IRS and finally, does the company need to declare any non-US income? - I can't think of any other documents that needs to be submitted to the IRS. Generally speaking you would not declare any non U.S. source income unless you were deemed a resident for tax purposes in the U.S.
Finally, could you recommend any tax lawyers/accountants who are able to assist the company to meet any legal obligations outlined above. - Unfortunately we cannot promote any other businesses on the website. It is part of our expert agreement with JustAnswer.
I hope this provides the clarity you were looking for, please let me know if I can assist further.