Will the USCIS deny a green card renewal due to child support arrears?

No - one thing hasn't nothing to do with the other.

As a very general rule of thumb, we do not file E-2 cases unless there has been an investment by the Applicant of a minimum of $100k.

If i get married in another state, can i use an out of state lawyer to help with my citizenship?

yes, we represent clients all over the USA.

I was approved for Deferred Action last year, will that help my application when my wife files for me?

Whenever you file a different immigration case, you have to take the bios again

How can I fix my status quickly? For citizenship or renew my expired green card?

There is no need to file for a new green card. You should file for naturalization. The process is now taking between 4-6 months.

Does deportation affect E2 application

It should not directly impact your E-2 but they may look at your immigration history

I need I130, I485 to apply for green card right? , I-765 for work permit? and I have no idea about the "guarantor" form. TY.

You will to file the I-130; I-485 and I-765 along with 2 affidavits of support from your husband and his father, assuming he qualifies.

F-1 student recently married needs advice on spouse visa

She can come in B status and change to F-2 status while in the USA if she so desires.

Can I keep my sponsor and file an O1 extension for three years?

You may file for an extension. You will need to submit all of the same type of documentation you previously submitted with the possible exception...

What happen if USCIS loses my I130 file? Are there another alternative to recover the petition?

It is really rare for this to happen? Did you pay the filing fee by check? was it cashed? If not, then you may need to re-submit the petition.