If you are in status, you can file for a change of status. The pending asylum application does not disqualify you.

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Do we need a valid passport for marriage based green card interview

No.

My fiance has no ssn, how can I marry him?

Apply for a marriage license and get married.

I filed an H-1B based on approved I-140 and pending I-485 and I had H-1B for more than 6 years, I am out of status right now.

If you have a pending I-485, why do you need the H1b?

H1B Petition and Previous ACD

I have never even seen this come up during an application for change of status. It comes up when you apply for admission into the U.S.

As of today, 06/19/2013, I have 951 days spent outside the US in the the last 5 years. How soon can I file N400? Thanks.

From the date of filing, count back for 5 years, and if your total works, you will be okay. Note you have absences over six months, and basically...

My I-130 petitioned by my spouse , a green card holder, was approved.

The National Visa Center is in the U.S., not your country. Notify them that you are in the U.S. and will seek adjustment of status.

VISA PETITION I130 issue

The California Service Center is sending I-130's to various local offices as well as other service centers for processing.

For how long do I have to leave the USA to switch my status from H2B Visa to ESTA?

There is not enough information to answer this.

We have given our fingerprints back in OCT but still havent heard back. It's been 9 months. What do u think the issue could be?

It depends on what application you are filing.