1. It takes... as long as it takes. Probably 4-6 months for approval of an I-485, maybe less, maybe more. If you petition for advance parole, travel may be okay if it's granted but remains iffy if there's going to be a period of ineligibility resulting from overstay.

2. Her G4 is derivative of your employment status, which is no longer in effect. I would be wary of trying to reenter on G4 status, even if her I-94 has not expired.

3. That's problematic given that she's seeking permanent residency. An F1 visa is a nonimmigrant visa, incompatible with seeking residency.

4. I don't see that she could qualify to file an I-360, if you've ended your employment with the UN.
Quote Quoting Special Immigrant International Organization Employee or Family Member
Certain long-term "G" and "N" nonimmigrant employees of a qualifying international organization entitled to enjoy privileges, exemptions, and immunities under the International Organizations Immunities Act, and certain relatives of such an employee, may be eligible to apply for classification as a Special Immigrant. To determine eligibility, contact the qualifying international organization or your local USCIS office.

The petition must be filed with:
1. A letter from the international organization demonstrating that it is a qualifying organization and explaining the circumstances of qualifying employment and the immigration status held by the person the petition is for; and

2. Copies of evidence documenting the relationship between the person this petition is for and the employee.