Yes, she will need to file a form 1040 that includes her income from worldwide for Nov and Dec 2024 or whichever date she arrived through the end of the year.
Yes, she will use her SSN as this number has now replaced the ITIN so anytime she does anything that needs a SSN or ITIN, she will use the SSN.
She would be a dual status alien since she didn't get her green card and arrive in the US until November and then left the country in January. She is not able to take the standard deduction so even if she doesn't make a lot, there would not be a minimum filing threshold as her only deductions would be itemized deductions and they would need to be listed in order to use them.
Her permanent address will be wherever she permanently lives and where the IRS can contact her or send her mail.
You can use TurboTax Premier to file her Resident Return,
Also, depending on which state she lived in while here, she may need to file a return for that state.
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