Hello my name is ***** ***** I am delighted to answer your questions today. I have 35 years experience as an immigration lawyer.
If the office refuses to extend my I-94 and asks me to re-enter the US to get a new I-94, can I visit Mexico (just to the airport and back to get a new I-94) with my current H1-B visa?
Yes, but you have to insist to the airline to surrenderyour expired I-94 so that when you come through inspections on return flight the CBP has to issue you a new I-94.
- What is my current H1-B status, given that I'm unemployed? I have a valid I-797 and my employer will rehire me immediately.
You are out of status and since your I-94 is expired the inspector can claim your visa became void under INA 222g
See this link
Usually you can only apply for a new visa in home country but read the above link which is the Dept of State Memorandum and you may plead your case that you expired under exceptional circumstances because you did not know that the I-94 was issued only until passport expiration date.
You may want to consider going to Canada instead since it is easier to fly to India from Canada if your visa is refused in the third country. Vancouver is usually a good post.
- If the office decides to void my H1-B visa, what are my options?
Only option is to find a new employer to petition you.
Of course, I am sure you understand your positive rating is very important to me as we are not on salary and that is how we receive compensation, you choosing a smiley face or 3+ stars
In the future, you may begin your questions with “FOR JUDITH” and I will be your personal immigration expert.