1. Best way is to file the I-130 petition for her now (in the States although some consulates will allow you to file it there) and let her consular process and obtain the green card in whatever country you are in. She has immigrant intent so it would be best for her not to come in on a non immigrant visa. Time frame from filing the spouse petition until issuing the green card could be as fast as 6-9 months depending on what country you are in and other processing issues.
2. See the attached link for procedures on notifying the consulate after the birth of your baby. Your child is a US citizen.
Best of luck to you and your family,
Law Offices of Patrice Dziire
Winter Park, Florida