While your wife can certainly petition for you, and you can apply from outside the USA, you are best advised to remain. You are able to pursue adjustment of status with the I-130 petition, even after you overstay, because you initially entered legally. Applying outside the country, since you are in overstay status, could render you susceptible of being barred from a legal immigration visa, as a policy of U.S. Dept. of State or Border & Customs Enforcement.
You would have to tell me how "long ago" your conviction took place. There are some instances that a fraud conviction can be waived if done before you had been a legal resident for at least 7 years, others exemptions exist as well. However, an aggravated felony cannot be expunged or dismissed for what appears to be administrative reasons. Like the other counsel said, an experienced attorney is absolutely needed for you at this time.
Your friend is in a bad situation. If he attempts to go back and is caught, he will be held, and probably processed out with an expedited removal order, which will make him likely to get a permanent ban that cannot be reviewed by even an immigration court or court of appeals. Unfortunately, he is in a position of having to remain in the country and wait to see if the proposed immigration reform law is successfully passed.
First, a C-1 crewman's visa blocks you from adjustment of status or any other legal visa, without departing the U.S.
Second, a Social Security number does not allow you to work legally, without a valid and unexpired visa, including the J-1.
You also cannot obtain a green card after first entering under the visa waiver program. But if you leave and apply for a B-2 travel visa and are readmitted, you can apply for work visas. Consult with an attorney before moving forward.
Hopefully you two are filing your I-130 with an I-485 (or I-765 work authorization) as part of the total package. She is petitioning for you as an Immediate Relative, so you mark part 2 application type A.
In addition to Messrs. Rothstein and Abbott, I would have to say that he may have a problem if he has no immediate family who are U.S. citizens or legal residents for whom he may claim a basis for relief before an Immigration Judge. But one thing for sure, he must insist, if he has been here for more than 2 years, that he be held over for proceedings rather than allow them to remove him. He may also be eligible for DACA-deferred action relief, too. But get him a lawyer, and fast!
If this was an adjustment of status-green card interview, say based on marriage, the USCIS interview agent should have granted a continued appointment-a rescheduled new time. To deem your application as abandoned, and therefore denied, that was really harsh. Unfortunately, you will have to either request a reconsideration of your application, which will cost over $630, or you will have to file a new I-485, which with past record now of denial, will be more difficult, for USCIS will consider...
The fact is that your country's embassy-consulate must approve the waiver of the J-1 2-year return requirement. The fact that you have already been here on a J-1 for 4 years, longer than the 2-3 years that are the minimum before the 2-year separation is imposed indicates to me, however, that you already may have been exempt, which makes your concern about getting an extension puzzling. You definitely will need an attorney for this matter.
Yes, as the others said, if he has no serious criminal offense record (felony, 2 misdemeanors, no drug or DUI), then he is eligible for DUI. Also, I would be wanting to know what the mother's status is. If she is legally drawing welfare and is not an illegal public charge, she may herself be a legal resident. I would really want to know what her situation is, and besides, she may be eligible for cancellation of removal, if she has been here for over 10 years. An experienced attorney would...
Even though the Motion to Reopen time period has passed, if the error can be shown as being egregious---really bad, then the USCIS can be requested to reopen sua sponte, on their own initiative, or get a motion to reconsider for your client, filed with the USCIS.