Since you are applying for your parents IV, DS-260, questions about you spouse are not applicable. Answer "NO" to both questions.

Yes. you can travel to Mexico for a week with an expired J1 visa and valid I797 for H1b.

A correctly and timely reply to the RFE guarantees further consideration of your application.

It is a mandatory requirement. Make an appointment and complete your biometrics exam at your local ASC location.

No. Birth a child does not speed up the process. If you think of other acceptable reason(s), try expediting your application on USCIS website....

Without looking at your immigration history, it is impossible to answer your question. If you think it is the local USCIS field officer, so answer...

Contact a lawyer to determine after reviewing your documents, which of your family qualify.

The two most common are family and employment-based approaches. Hire an attorney for further guidance.

It appears you don't fully understand the AOS process. It is wise to hire a lawyer for further guidance.

Yes you may refile your application with proper filing fees. Good luck.