My school assured me of sponsoring H1B before and after hiring but did not file the H1B. Can i take this case to the court ?

You should consult with an employment/labor attorney and then an immigration attorney.

Instead of filing H1 can they file directly green card for a company and how soon will that green card will come if its current?

This is theoretically possible, but depends on a number of eligibility factors that must first be assessed.

I accepted a voluntary departure,how long do I need to wait before I am eligible to apply for a visitors visa?

Probably many, many years depending on how long you stayed "over time."

If we file an I-140 with an employer, and then get married and want to apply for GC through my citizenship, is it a conflict?

There is no inherent "conflict" in filing two different petitions. Consult with an attorney to discuss the necessity for or wisdom in doing either...

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Question about F1-Student resident alien status

There are many different types of immigrant visa petitions that may allow a person to become a lawful permanent resident. Consult with an...

Student visa

If you have an F-1 visa, she should be able to acquire an F-2 dependent visa.

Hey! Plz help me ! My pd is sept 27 2013 for F2a India

F-2A for India is backed up to May 2012 as of June 2014.

Hey! Plz help me ! My pd is sept 27 2013

This depends on what category your petition falls under.

Do the funds for EB-5 investment have to come from outside the US?

You must be able to trace the source of funds to legal sources.

H1B vs. family-based green card and EAD?

If you are eligible for adjustment of status and properly file an application, you should receive an EAD within 90 days. You can work after that...