Currently, Addis Ababa Bole International Airport is the only port of entry for e-visa when you apply Ethiopian e-visa online.

Yes, a yellow fever vaccination is required for entry into Ethiopia. Other countries listed in https://www.who.int/ith/ITH_Annex_I.pdf.

In the event of traveling with a child, one must make sure that one is in possession of said child’s valid birth certificate and/or adoption certificate.

You can apply Ethiopian e-visa online while still in Ethiopia, as well. Overstaying your visa can lead to fines or even imprisonment. Passengers are allowed to request an extension (before the visa expires) by traveling in person to the Head Office of The Main Department for Immigration and Nationality Affairs (Addis Ababa, Ethiopia).

The validity of an e-visa starts from the day you enter Ethiopia, rather than the date of issue.