Generally speaking TSA does not check immigration status, they just need a valid ID. SO if you are not traveling internationally and do not need to clear Customs risk is minimal despite being out of status. That being said, there still is some risk, however slight.
You should go by what the Nepal government has told you as Nepal has its own immigration laws and standards for travel into the country. You should consult with your immigration lawyer for more information about applying for additional travel documents at this stage of your asylum process.
If he is applying for Cancellation of Removal the form you are required to fill out does ask for specifics regarding government assistance. A good immigration attorney can use the fact that you and your children had to go on govt asst due to lack of financial support during his incarceration as proof of financial hardship the kids will face without their father's support. You need to hire a good immigration attorney to represent him for this matter. Cancellation of Removal is a very hard to...
Agree with Neil, you need to address in the cover letter and back up with documentation, i.e. birth certificate. You may want to highlight/bold the text alerting NVC to the administrative error.
Grady G Gauthier
First, don't panic. USCIS will likely send you a request for further evidence (RFE) to correct the mistake. They may also ask you for other evidence regarding your case. If this happens I recommend you contact an immigration attorney of your choice to schedule a consultation so all relevant facts can be analyzed and competent advice given.
Agree, you can work from home in a foreign country and still be on payroll as your H-1B will not be in affect once you are off US soil. You should also be able to take unpaid leave while you are away, it should not be considered 'benching' as you are not in the US, especially if it is documented as leave for some kind of personal reasons rather than an employer sending you off. You should maintain your plane tickets and all other documentation regarding the trip.
A business visa is for coming to the US to conduct and or go business meetings, look for opportunities, etc., it does not allow one to work for pay in the US. You may have options if you would like to start a business in the US and earn money here like an E2 treaty trader visa, but this depends on if your home country has an applicable treaty with the US. I highly recommend you have a consultation with an immigration attorney to develop the best strategy for your needs and goals.
If no cDV harges were pressed and all DV charges were ultimately dismissed he should not have an inadmissibility bar based on this alone. You should work with an immigration attorney regarding providing the proper documentation and legal arguments to the US Consulate abroad.