Applying for adjustment of status within the US.

If the petitioner on the I-130 is your immediate relative, then that sounds good. These cases can be complicated, so it might be worth your time...

I got my approval notice in dec 9 2013 but till today 5 feb 2014 I dint get any letter from Nvc !

It can take a little while, and it doesn't mean that there are any problems. Give it another week or two. If they still give you a problem, it...

Naturalization

Sounds like you're fine as long as you meet the other eligibility requirements. Here's the USCIS webpage with links to the N-400 and instructions....

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Will my brother be able to sponser me to be a US citizen?

He can file an I-130 petition to begin the process. It will be a very long process. Many years.

No. This is not true. You can go ahead and proceed.

A permanent resident was arrested and charged with theft. Charges were dismissed, can immigration charge him with invasion?

Theft is serious, so best to bring all court documents to an immigration lawyer who can review them. Charges can be "dismissed" for state...

Will a arrest and guilty plea for disorderly person affect getting green card under new immigration reforms?

Just keep your records for now. If and when reform is passed, post again and we will have a better idea of how to answer your question.

Hi, I have petitioned for my sister to come to the united states and she is already approved as of december 19, 2013.

Please see the Family-Sponsored table here: ...

I have a joint sponsor what is he supposed to put in part 5 of i864

The joint sponsor, filing his or her own I-864, answers the questions based on his or her household size.

Will an old shoplifting charge (16 years ago) affect my wife's adjustment of status decision?

It depends on the crime and the disposition. I'd recommend bringing the paperwork to an immigration lawyer before filing the I-485, just to be safe.