The I-765 is an application for employment authorization. There are several dozen different eligibility grounds for this application. You should speak with an attorney about your husband's eligibility for employment authorization and his immigration options in general.
The answer is yes - even if a prior waiver application is denied, the new waiver application can be approved. It depends on the reasons for the denial and the strength of the new application. When clients come to us with denials of applications they prepared on their own or with the help of another attorney, we help them identify the areas where the new application can be improved.
To naturalize, you have to meet physical presence and residency requirements. It sounds like you might have a hard time doing so. You should also be concerned about having abandoned your lawful permanent resident status. You would do well to hire an experienced immigration law attorney to help you with these issues.
Also, were you issued the 2 year conditional green card or the 10 year "full" green card?
For a marriage-based permanent resident, it should generally not make a difference in terms of naturalization eligibility if the permanent resident went to school versus worked after obtaining permanent resident status. For tax questions, you should speak with a tax professional who is experienced in assisting foreign nationals.
You need to be qualified for an immigration status that would allow you to work and you need to be admissible to the U.S. The answers to both of these questions require an in depth analysis, including a full review of your immigration and criminal history and a review of your plans once you arrive in the U.S.
Your attorney should be able to answer this question for you. If your attorney cannot, then you need a new attorney. The premium process clock will restart upon the USCIS's receipt of your response. It will have 15 days to issue a decision, take some other designated action, or refund the premium processing fees.
Congratulations on your pregnancy. By DV1, I assume you mean that you won the visa lottery, so double congratulations. You can enter the U.S. single and pregnant. Things become more complicated (but not impossible) if the child is born before you immigrate but if you immigrate and then the child is born here, there should not be a problem.
If you decide to marry the child's father, you should speak with an immigration attorney before you marry to discuss the various options you would have...
You can start the petitioning process from abroad. If your husband needs an affidavit of support, though, by the end of the petitioning process you will need to be domiciled or prove that you will be domiciled in the U.S. when he is ready to immigrate.
Whether your child automatically acquired U.S. citizenship at birth or needs to be petitioned along with your husband requires a more detailed analysis.
Very specific requirements have to be met before a U.S. citizen can lose her...
You will have multiple options for you if you divorce or separate from your husband, including if you entered into a good faith marriage and the marriage entered in divorce, you entered into a good faith marriage and he abused you, or your removal will result in extreme hardship. You may also be eligible for other forms of relief. It would be in your interest to speak with an experienced immigration attorney about these and other options.
Visa Waiver entrants give up important rights, including the right to contest removal other than through an asylum claim, so by failing to leave the U.S. when required you are risking a summary removal by Immigration and Customs Enforcement. With good counsel and some luck, you might be able to avoid this and obtain lawful permanent resident status without being removed or triggering a ban.