Yes, you can travel abroad on H-1B while I-131 (Advance parol) is pending based on Family based I-485.

I concur with the above assessments, and you may have a good case.

Ihttps://egov.uscis.gov/processing-times/ Should not be confusing. Check processing times of your case above link.

The F1 application would be subject to heightened scrutiny due to the immigrant intent problem. The outcome of the application will depend on the...

Yes, there will be problems with CBP at POE.

Yes. Probably with the receipt of I190 you can file N400.

Write to USCIS an tell your side of the story. It will amount to credibility and conclusions would easily be ascertained.

Communicate your good faith effort to USCIS.

Probably no waiver is required on your case.

Yes, wife can travel to the USA on H4 Visa while her H1B visa is in processing or got a 221G.