The $13,825 is your GROSS income (total rent BEFORE deductions). If your gross MN income is under that, you do not need to file a MN return.
If you will not owe any MN income tax, you don't need to make MN Estimated Tax payments.
For the Federal tax, yes, you would give the Form W-8ECI to the company that is handling the rentals (AirBnB or whatever else).
Yes, you will need to attach a statement to your tax return.
The US version of TurboTax is not able to file tax returns for a person who is not a US Citizen or US Resident, so you will likely want to go to a tax professional that is experienced with that type of situation.
