Do I need to go for a re-stamp when my status changes from H4 to H1 ?

If you travel outside the US you would require an H1B stamp to return to the US and be admitted in H1B status for H1B employment.

Can I switch jobs while keeping the same I-140?

if you switch jobs you maintain the I-140 priority date. Your new employer would need to its own PERM/I-140 for permanent sponsorship.

If the W-2 also shows each of you receiving the W2 at the same address it is helpful.

H1b extension and perm

We would not expect the prior application to be acted upon first.

Can i still apply for OPT extension before May2016 if my position is unpaid?

Unpaid STEM positions may qualify for the 17 month STEM extension before May 2016. Check with your DSO when updating your I-20.

You need to act fast. Consult an immigration attorney with your employer about what actions you may take.

Authentication of documents

Officers make mistakes. Your green card may be at risk. You should consult an immigration attorney.

First time stamping is better done in one' home country. US consulates in Mexico were not doing first time stamping. You have to check if they are...

Can I ?

You may sponsor both your daughter and son. Current wait time to obtain a green card once you file is about 7 years and longer depending upon...

If someone came here illegally, would they qualify for the 485 form and waiver?

I'm not sure we understand the question. If a Welcome notice was received and a green card issued, but not picked up the person is a green card...