If she is a U.S. citizen, she can travel with a U.S. passport that you will need to obtain for her and a signed permission from you, as her parents (without it, they may suspect that the baby is being stolen).
Most likely. I suggest that you schedule a consultation with an experienced immigration attorney and bring copies of your entire file. The attorney would need to look at the history of your case to provide you with specific advice.
Yes, this means that the H-1B petition has been approved. The company should be getting the formal approval notice in the mail. Keep in mind that if you were also asking for change of status within the U.S., this does not necessarily mean that the change of status request was granted. If it was, the approval notice must contain your new Form I-94.
Gregory Romanovsky, Esq.
12 Marshall Street
Boston, MA 02108
There is no "6 months" requirement. The quicker you leave, the more suspicions the immigration service may have at the naturalization stage, but if you have documentation as to why you had to leave, you should be fine, even you leave tomorrow.