Are private research universities exempt from H1b quota?

it really depends on the University and whether they are a non profit as defined by USCIS

How to obtain my residency ?

You must see an attorney. It may be possible to get parole in place

I have a j1 visa for two months now.Can i change status?and how soon?

depends if you are subject to the 2 year home residency requirement. You cannot get a b visa for volunteer work

I'm a U.S. citizen, married to a brazilian, she is 10 weeks pregnant and we wanted to have our baby in the USA.

Consult an attorney. She may be denied entry if you have filed an I130 for her as this evidences immigrant intent

When should I file I-751Removal of Conditions with divorce waiver when my husband and I are divorcing

You can file on August 24 2015 and must provide your divorce decree and evidence of a good faith marriage while married

I have heard about commonsense immigration reform and am wondering if it helps US educated nurses who want to stay in USA.

We hoefully will know something on November 21st

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Will there be a problem if the one who is sponsoring my education in usa in a us citizen friend of family?

That is unlikely to be a...

You may be able to just mail your renewal application to the Consulate in Washington and do renewal through a passport agency

AOS approved then two hours later "reopened for reconsideration.

Hire an attorney to assist you and do an info pass to check what is going on

Have Valid H1b stamp ,H1b Transfer pending with RFE and Need to travel to home country?

1. Possibly. It depends if company A has revoked your visa. Port of entry may want to see your last 3 pay stubs and if they are not from company...