Does USCIS know if a lawyer is accredited for G-28?

You should use a reputable lawyer who is admitted to the state bar.

How do i travel outside united state?

You will need your valid passport and green card for short travels like this.

Yes a withdrawal should not detrimentally impact a subsequent filing however you must be eligible for the visa you are applying.

Upgrading Green Card case for Spouse after becoming the US Citizen

Yes he should upgrade the petition and yes would need to file for his children at that point.

What is means by written statement to the embassy outlining the circumstances beyond control?

Yes you should contact the Embassy right away to inform them of delays in the submission of requested documents.

Spouse naturalization after becoming us citizen

No the three year rule applies if the LPR has LPR status and is married to a USC during that time.

What's the processing time?

You should follow your lawyers and the officers advise and await about a month for the mailing of the green card.

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How it works?

Yes it depends on the category under which you filed.

How to apply for visa change of status from F1 to green card after marriage?

It depends on your status in the US. It is best to use the search tool on the Avvo website to find an experienced attorney. Good luck.

What annual income should I use for I-864 if my job changed in middle of this year?

It should be your current income with your new employer.