If she wants to take out a loan, go to a bank and ask what the requirements are and what the terms are. I think you will be very disappointed that you can’t qualify or can’t afford the loan. Unsecured, personal loans usually have high rates and short repayment terms.
You have issues with immigration which haven’t been resolved. I don’t think the green card will come as quickly as you think since you had to answer that you had overstayed a visa. They don’t like that. Don’t borrow anything until you have that green card and then stick to government student loans.