Can you handle with the expedite Citizenship application. Current Status uncertain.

She needs to file an I-90 Form to receive the green card you are saying she never received until now, most likely because she changed her address...

Can B-2 visitor visa be extended beyond 1 year?

No, regulations to that effect do not allow for a B-2 visa to be extended beyond 1 year, unless an exception is made (rarely, if ever, and...

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Getting a Second Masters from US, can I enter with the Same F1 Valid Visa and New I-20?

Yes, no problem.

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Can my husband get in to USA with his previous 5 years multiple/B1 visa(i130 petition is on process) ?

In all likelihood he will be denied entry to the US.

No, you do NOT need to leave the US, you can file for a change of status with USCIS here. You will need to apply for a consular visa stamp abroad...

Is it true that the removal of conditions of green card is done automatically by the USCIS

Your question is unclear. USCIS does NOT send any "notice" for the need to remove conditions within 90 days of before the GC's expiration.

You are in removal proceedings in immigration court due to your asylum application having been denied by the local asylum office. You are thus...

Immigration

4 between 6 months, depending on how busy the NY district office is.

I-94 Stay

Once admitted to the US, it is the I-94 card that governs the terms of your stay in the USA.

Which options is available for me j1 visa to work part time

The J-1 visa is the only option.