Tuition at the rate the institution assigns, fees, books, and any health coverage the school requires, all against the principal's income alone. Because TD does not authorize employment, a paid assistantship is not a way to offset those costs while holding that status.
Budget on the tuition rate you were quoted
Non-resident rates are frequently the starting point for a newly arrived household, and any change depends on institutional and state rules rather than on immigration status alone. Ask the bursar's office for the classification in writing before enrolling, and budget on the quoted figure. Scholarships that require no services may be worth exploring; those that require work are a different matter.
The regulation requires that a degree from an institution outside Canada, Mexico or the United States be accompanied by a reliable credential evaluation, which is a private service with its own fee and turnaround. Ask for written scopes from every professional involved and place four columns in the budget: contract negotiation, immigration analysis, evidence production, and government or travel charges. The TN admission fee is listed on the USCIS fee schedule, while state licensing, examination, credential verification and the health-care certification are charged by other bodies and usually cost more in total.