What constitutes abandonment of the EB-5 application?

You should carefully plan your travels. You may wish to consider consular processing based on these facts, but consulting with an immigration attorney will put you in the best position.

Based on the information you provided, you may delay filing your I-485 (Application to Adjust) until you return to the country. The delay in filing your I-485 does not mean you have abandoned your EB-5 petition. The issue of abandonment is real and involves a failure to file I-131, Application for Travel Document once an I-485 has actually been filed. The general rule governing abandonment is that, if your I-485 application is pending and you plan to travel out of the country, you must also file your I-131 (Application for Travel Documents) before you proceed to travel. Upon filing I-131, you can either wait for the approval in the United States or choose to pick up your approval from the U.S. Consulate abroadthe one in Mexico, in this instance. If you fail to file I-131, either at the same time you file your I-485 or before you leave the country, your I-485 will be considered abandoned. It may also mean that your EB-5 petition has been effectively abandoned. Consult an attorney for further clarification of your travel plans and differences on when an abandonment can actually occur.

Abandonment of an application would consist of filing the I-485 first, then leaving the United States without advance parole (or an H or L visa). That would effectively abandon your I-485 application. What you are suggesting will not result in the abandonment of your I-526 petition approval or any other application. As long as the purpose of your entry is to resume your O-1 activities, then you should be admissible to the United States based upon your O-1 visa. After you are admitted in valid O-1 nonimmigrant status, you could legally elect to file your I-485 application for adjustment of status based upon your approved I-526 immigrant petition.

Given the fact that you have a valid O-1 non-immigrant visa, you are eligible to be admitted to the United States in O-1 status and once admitted, you would be eligible to apply for adjustment of status, assuming visa numbers are available, based upon the approval of your husband's EB-5 petition on Form I-526.

You appear to be correct. Alternatively, you can file the adjustment of status package with an application for a travel document. I need more information, however, to provide you a better case assessment.

You have it more or less correct. The O-1 is not a dual intent visa, it is an "in between intent visa." So after you file the adjustment, you cannot travel without an approved advance parole, and that can take at least three months to process. You will not be deemed to have abandoned anything unless you file the adjustment of status and leave without obtaining the advance parole. You will not likely be refused admission because you have an approved immigrant visa petition.

Traveling on your O-1 visa after the I-526 is approved is not an abandonment of your petition.

That should be fine especially if you do not need an O-1 visa.