No, change of passport is unlikely to affect lottery visa administrative processing.

Contact USCIS for your record update with supporting documents.

Yes, the I-539 is required for H-1 to F-1 is filed by applicant not the employer.

You are required to have a valid PRC or receipt of I-90 at all times.

You are on the right track. Consult with a local lawyer for guidance.

Yes, if your income meets eligibility guidelines of 125% of USCIS poverty guidelines.

You may also call USCIS at 800-375-5283

Consult with a lawyer for a comprehensive comparison of each approach.

It depends on multiple factors, as a result hard to predict.

You have a complex case that warrants consultation with a lawyer.