Citizenship ?

Usually 3 to 6 months. You can check processing times on the USCIS website

I485 : birth certificate not available, Indian citizen

if the birth certificate is available you should present the birth certificate

Contact another immigration attorney more information is needed as an approved I-130 alone does not permit you to remain in the US.

Contact the US consulate and notify them of the error and ask them to either modify the error or cancell and refile.

Can I risk my mother to have an overstay here in US when my application for citizenship can be obtained in just a few more month

You should discuss your situation with an immigration attorney in a private consultation.

How soon can my mom come back after being in US for one year?

The issue is not when can she return but rather is she a resident in the US or in her home country. By spending significant amount of time in the...

How long is it taking to Administrately close a removal proceeding?

Your removal proceeding should be terminated before departing. The timing is much to the discretion of the particular immigration court and the...

Which forms I must apply ? or if there is any why I get a one year visa until the green card process finished ?

If you are looking to obtain resident status or US citizenship for you children being out of status if they are under the age of 18 should not...

Employment outside the H-1B is not permitted.

How do I withdraw my application and submit a new application because of a mistake I did previously on filling ds260?

You may have more success trying to notify the consulate of the error than trying to withdraw. The record remains regardless.