Can I go ahead,get married file CR1 or I go ahead refile I -129F without addressing the consular concerns for refusing a visa?

Yes you can refile but perhaps a consult with an experienced attorney is a good idea first.

Yes you can own the business in India while staying in the United States on the H-4. You cannot be employed in the US without an EAD though.

I94 extension due to passport renewal

You will need a new stamp. Contact your company's attorney and ask him this question.

Im gonna get married my finance who is coming on k1 visa

You need to get married within 90 days of his entry to the United States. Once that happens you should file for adjustment. There will be a...

Are there any chances if I marry my girl friend and start my process again.

A finding of marriage fraud will prevent you from having a new I-130 visa petition approved. You need a lawyer to help now.

My passport expires in 2017. Do I just need to renew my passport and use that as proof? Is a passport proof of citizenship?

You may have problems if you travelled on an American passport. You are eligible for social security even as a resident. Meet with an immigration...

What do I have to do or is there anything I have to do in order to get married?

You can get married at any time. If he is a US citizen then he can start a process for you to get a green card. You will need to apply for...

Is marrying a US citizen repeal my asylum case or affect it and how?

Your asylum application will continue. You can marry and this should give you another option for staying in the US.

Immigration may know about all dismissed judgments?, or I have to let them know about it This woman is a real burden to me,

You will have to provide this information to USCIS if you want it considered by them.

What are our options? should apply for a duplicate copy? because I don't know USCIS ever sent the approval notice to my address.

You can request that USCIS send a duplicate copy. There is also a form you can file to make the request.