My girlfriend committed fraud by working and not going to school with her F1 visa. We want to get married now. Out of luck?

We would need more information to be able to help you. There are various factors that can be very prejudicial for your girlfriend, such as filing...

Is it OK to fill out the background check form at the school and have them send it ?

I agree with my colleagues.

How long is the waiting time for a foreign medical graduate when he is Adjusting his status from F-1 to J-1?

I agree with my colleagues.

Can I apply in EB2 category in future???

Your best bet is to consult with an immigration attorney in person since there are many factors relevant to your case that need to be considered...

Any good news or updates on immigration reform or may be when there will be any announcement or plan lay out?

There is a good environment for immigration reform, but still need to wait and see what congress does this year.

What are the birth certificate replacement documents to file for the immigration ?

I agree with my colleagues.

If the denial was in error you may ask USCIS to reopen the case sua sponte (on their own motion), or to preserve your right to reopen the case you...

Check Status for Form I485 Online

I agree with my colleagues. There's good indication that your case was approved.

Social security number for kids if I have E2 visa

I agree with attorney Devore.

I lost the i94 attached with i797a form,but I still having my i-94 when I enter USA. Do I need to make a replacement?

The I-94 number should be the same. Therefore you may use the one you have. You can also request USCIS to send you a copy of the one you lost.