If you are out of the country for 330 days in 12 months, then you could be considered an Expatriot, if you also have established a home in another country.
In general, a US Citizen is required to file form 1040 to report their income from worldwide sources whether or not they reside in the US.
You would need to file as a nonresident for each state where you are earning money. If you are simply holding the property, but not renting it out and making money on it, you would not file a return for the state simply because you have an investment property there.
Yes, you need to use TurboTax Premier to report investment properties.
For state of residency, you will select Foreign.
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