You can find the requisite form on www.uscis.gov. Be sure to apply for the extension prior to the date indicated on your I-94 card, not your visa expiration date. You will also need to include evidence of your ability to financially support yourself while here, and your intention to return home. I recommend consulting with an immigration attorney before proceeding. Good luck!
Because you are married to a US citizen, you are eligible to apply for your green card without leaving the United States. It's impossible for us to tell you what your chances of getting approved may be without reviewing your immigration history in full. You should schedule a consultation with an immigration attorney. He or she will be able to determine if there are any disqualifying or complicating factors in your case based on a full review of your case.
There is much more to every immigration case than simply filling out the forms. There are very strict deadlines that apply to the process of obtaining a green card through the DV lottery, and you would be well-advised to hire a lawyer to advise you of these deadlines, review your individual immigration history for disqualifying factors, and prepare your case.
Based on the facts you describe above, it is most likely that you will need a waiver to enter back into the United States. Waivers tend to be complex and this matter is best handled by hiring an immigration attorney to assist you.
As a citizen of Cuba, you may be eligible to get your Permanent Residence under the Cuban Adjustment Act. Consider consulting with an immigration attorney for a full analysis of your eligibility for this benefit based on the individual details of your immigration case.
I agree with my colleagues. Every day that you are out of the country counts, regardless of whether it was in the same year. You would be wise to have an immigration attorney review your travel history, help you calculate the total time you've been out of the U.S. and identify any other possible problems in your case before you apply for citizenship.
Your case has been re-opened, meaning you do not have to re-file a whole new application. However, it also means that you will need to learn the reason for the denial and submit a response, likely in the form of a legal memorandum and evidence. You would be wise to invest in hiring an immigration lawyer.
Yes, you can continue to work in the U.S. while you are a lawful permanent resident. As my colleague correctly pointed out, you may find yourself charged with abandonment eventually. If you lose your lawful permanent resident status, you will no longer be able to work lawfully in the U.S., unless you obtain a work permit through a valid visa. You may consider either structuring your financial affairs and ties to the U.S. in such a way as to minimize the chances that you are charged with...
You'll be much more likely to get the results you want by appealing the decision (if there's still time) or re-filing the application than by suing the Immigration Service. You are correct in that there is no requirement under immigration law that a couple live together before their marriage ceremony; the key inquiry should be with respect to whether, at the time they entered into the marriage, the couple intended to make their life together as husband and wife. However, it sounds like you...