It can take 30-90 days for NVC review.

No not based on the unlawful presence.

Refusal is that the documents were refused for some reason vs AP is that the case needs additional review.

She domestic travel she should have a valid passport or government ID for travel purposes.

Best to work with a family law attorney for guidance.

This is a valid basis for expedite with proof of the information you have provided.

After so many years, a new application may be requested.

You can upload to the online USCIS portal.

Contact NVC directly through their website to notify them.

No this should not present problems at port of entry.