1. Great news! You absolutely can. Spouses of US citizens are deemed to be "immediate relatives" ("IRs"). IRs are not required (or expected) to maintain valid non-immigrant status. Also, any IRs are never penalized for any previous periods of unauthorized employment. Your spouse can immediately sponsor you for the Green Card. If everything is done correctly the first time, you should obtain your GC in 6 months or less! You will not have to leave the U.S., unless you'll later want to, with a green card in your pocket..
2. Why would you want to after what I explained in 1. above? You can continue to work with the same employer if he is not afraid to employ you without authorization (you are an IR, but it is the employer who risks "sanctions" and "penalties" for knowingly employing someone who is no longer authorized. Once you file for your marriage based I-485, however, which could be next week, as soon as you have your medical results in your hand and your spouse completed the I-130 and the I-864 Affidavit of Support on your behalf, you yourself will be filing for a work permit at the same time, on Form I-765, which is normally issued within 2-3 months. You can legally resume working then.
3. As explained in 2. above, 2-3 months from filing.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Invite your spouse to a fascinating visit of the local immigration attorney's office. It might answer a lot of questions, assuage fears and concerns and believe it or not, even help with your situation. It will not be free as posting on AVVO. Well, but it might bring realistic practical assistance to your cause.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
1) You can stay based on a one-step filing (I-130/ I-485 packet)
2) You cannot appeal the H-1B denial, only the employer can.
3) 90 days from filing the correct packet with all the requisite forms.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. You are encouraged to seek independent and private counseling for a complete review of your case.
You should immediately file based on your marriage and I assume you last entered the US legally so the case will be processed in the US and you will have work authorization in 60-90 days. And you need a new lawyer immediately as well.
1. Marriage by itself confers no immigration status: your USC spouse must file a petition for you & you must file for adjustment of status based on that petition.
2. Appeal from denial of an H1B petition must be filed by the employer, not the beneficiary, and a pending administrative appeal confers no current visa status nor work authorization while pending.
3. If your application is complete & properly documented, about 4 months.
This is general information only. It is not intended as a substitute for legal advice, and does not create an attorney-client relationship. For legal advice specific to your circumstances, you must consult an attorney in a confidential setting, not in an online forum.