You will not get in trouble for reporting someone to the US Immigration authorities, but you may have better luck insisting that she move out.

SSI + Immigration

You should contact the agencies involved in disbursing the benefits you discuss, such as the SSA.

I'm going to divorce +move in a different state before my 2years GR.CARD expire.what happens next?After 2 years I have to leave?

You may want to explore the possibility of seeking a waiver f the joint I-751 filing requirement with an immigration lawyer.

Wandering about immigration policy and drivers license? Visa Immigration

Each State has its own rules for issuance of drivers licenses.

Travelling abord

You can lose your green c rd if you travel to the country of claimed persecution or stay out of the US too often or for too long on any particular...

Regarding H4 and H1B Status, please suggest

If she wants a social security card, she must be in a work-authorized status, such as H-1B.

I was threatened and coerced into helping my soon-to-be-divorced wife get a temp green card. How can I get out of sponsorship?

You cannot withdraw the affidavit of support at this stage. the only way to avoid responsibility is if she loses her status.

Is it okay to file the I-130 and I-485 when you are not living together? *see details

Yes, it is possible. You just must be prepared to answer questions about your living situation, which the USCIS training manual may consider...

I'm filing Form 751 90 days in advance of my green card expiration, but processing time is 6 months. Should I file sooner?

If you are submitting a joint filing, it will be rejected if you file it prior to the 90-day period.

Did medical school internationally, and residency training in USA. When applying for H1b, does it fall under advanced /regular?

Probably regular, but this may be a moot point unless you are seeking a visa for FY 2016.