You should file your taxes jointly with your spouse even if you have no income. All this means is that your spouse would add your name and personal information to the tax form. This is advisable not only to get a better refund, but also if you intend to apply for citizenship in the future. Also, if you need to remove the conditions on your green card, you will have the tax forms as evidence that you share a life together.
No, you are not eligible for U.S. naturalization while you are on probation. You should wait until your probation has ended before you apply for naturalization. At that time, you will need to provide information to prove that you served your time and that you have been rehabilitated. Given your conviction, I'd recommend consulting with an immigration attorney before you apply for citizenship.
Even though you are DACA approved, you will still need to fill out the same paperwork, pay the same fees, and leave the country to interview for your green card. Depending on whether you accrued unlawful presence before you were approved for DACA, you may need to apply for a waiver. This can be very difficult. You should consult with an immigration attorney who can help you.
Are you a U.S. citizen? If so and if he came on a valid visa (even if now expired), you can file your I-130 and I-485 adjustment of status application in the United States and without him returning to his home country. You can apply for a work permit at that time as well. You might want to hire an attorney to help you with this. Good luck!
You will need an immigration attorney to assist you. Depending on how your husband entered the U.S., it might be tricky. You will need to file an immigrant visa petition and a waiver application. You may be helped by the new provisional waiver of unlawful presence.
Feel free to give my office a call. We are next door in Medford, MA
I'm changing the category in this to immigration law. A consultation with a good immigration attorney will probably only cost $50-150. Both his plea and the final outcome of the case WILL have ramifications on his ability to stay in the US in the future and it is very likely that Immigration and Customs Enforcement will be notified that he does not have legal status in the US.
It sounds like you should consult with an immigration attorney about advice about your individual situation. Your felony involves fraud (a crime of moral turpitude) so it could trigger placing you into removal proceedings. Whether or not you will be placed into detention may depend on your immigration history, but chances are you will be allowed to stay at your residence if you are placed into removal proceedings as long as you are not a flight risk.
You should read any document that you are asked to sign, but you shouldn't be asked to sign anything that isn't routine (your I-485 application or affidavit of support, for example). USCIS has no reason to try to "trick" you. Just be prepared to answer questions about your spouse and your marriage. Good luck!