Yes the child born to USC May acquire citizenship. Consult with an attorney for guidance.

Yes upload the documents to the affidavit of support section.

It can be 2-3 weeks. Be patient with the process.

Yes, this error will be questioned and could be an issue for a subsequent application.

No, as this was a one time trip this should not cause a denial of the application.

Yes this would be questioned but could still be filed. Best to consult with an attorney for guidance.

No this is not public knowledge so your father should not be informed.

Yes departure from the US constitutes abandonment of the application.

Yes your sister should be able to bring your child with you during her travel.

Extended travel, marital status changes or criminal issues.