I agree with my colleague. The H4 is connected to your H1. Contact your company's US immigration attorney.

Will I be eligible for a H1B transfer or are there chances of going back to my home country for consular stamping ?

I agree with my colleagues. Contact your company's US immigration attorney.

Can employer file for H1-B while H4 is Processing/Pending?

I agree with my colleague. Contact the company's US immigration attorney for assistance with the new H1 filing.

Which date counts for 30-day grace period? Does the J1 sponsor have the authority not allowing me the 30 day grace period?

I agree with my colleague. The 30 day period cannot be changed.

File N-400 and change address or maintain previous address?

I agree with my colleagues. Contact a US immigration attorney for review and to make sure you meet the 90 day residency requirement prior to filing.

Can I apply for F2 while my h1b is in process?

I agree with my colleagues. Yes, you can apply for F2. Keep track of the H1B. Contact a US immigration attorney for assistance.

If I switch jobs while my spouse's greencard application is processing, will that likely cause problems?

I agree with my colleagues. It does not affect your pending petition.

Naturalization interview and stamps on passport from certain foreign countries.

I agree with my colleague. Contact a US immigration attorney for assistance prior to filing. The application must be completed truthfully.

What is best to this situation ?

I agree with my colleague. Your mother will have to prove non-immigrant intent. Contact a US immigration attorney for assistance.

I agree with my colleagues. There is no social security number update.