Yes you may apply, however, with all the time she has spent in the US there is a good possibility the extension may not be granted.

If your wife does not have pay stubs so respond. If the request is for your pay stubs you need to provide them.

When

Somewhat depends on how quickly response are provide to requests. Generally 5 to 9 months

It is extremely unlikely that residence status will be granted if your spouse does not attend the interview. Attendance at the interview in of...

Travel outside the US is not permitted. Entry requirements for Guam are the same as for any U.S. destination. Although U.S. citizens are required...

How much is the USCIS fee to file a VAWA for a woman and a minor child married to a USC ?

She needs to get to a safe place with the child, then she should discuss with an immigration attorney and domestic relations attorney.

Do I need to put that I'm married on my Citizenship form?

If married or for any question you must reply truthfully.

Is it illegal to work online while on the student visa?

Employment as an F without authorized employment is prohibited.

H4 expired 1/2/17 company didn't file for H4 with H1 in Dec 2016. I am 176 days in?

If you depart the US before 180 days of unlawful presence, you will not be subject to a possible bare of 3 years before being permitted to return...

H- 4 cannot be submitted without the H-1B being filed. Concurrent is permissible.