Yes, but you should notify the Embassy sooner rather than later.

Can H4 visa holder have any chance of job opportunities

You will need an employer willing to sponsor you fro your own H-1B.

I used to have a medical card, I was approved for the Dream Act will it affect me later if I want to get a green card?

It could, since anyone "likely to become" a burden on the Government can be excluded from the US.

Are my two(2) adult sons in the Phil. eligible to re-apply US Citizenship under 8U.S.C 1401g, USCIS Policy Manual, Vol 12?

These are complicated cases. Consult with an immigration attorney and provide all relevant documentation to aid in the analysis.

I have an overstayed j1 visa with 2 year rule- My profession was in the skills list.

If you are not eligible for a waiver, you will have to wait outside the US for two years and then pursue a visa.

Probably not.

My petetion f3 is on current but my b1 visa is already expired

This depends on whether you are eligible to adjust status under Section 245(i). Consult with an immigration attorney.

I'm married and husband is undocumented with more than three misdemeanors, is there anything I can do to help him become legal.

You can petition him for a green card. His convictions do not appear to render him inadmissible to the US. Consult with an immigration attorney.

The more compelling the initial evidence, the better chances are that you will not get an RFE. Try and get a letter from her treating physician...

What will be best and faster to apply for a green card, thru my Residence Mom or US Citizen Sister?

Most likely it will be faster through your mother's petition. TPS is not relevant based on the facts you provide.