How can I stay in the U.S. with an expired OPT extension but a pending I-526? 

Generally, an I-526 petitioner cannot stay in the U.S. with an expired OPT. Such presence will be illegal, as the petitioner will start accruing overstay, which essentially means you will be out of status. If that happens, you will not be able to adjust in the U.S. (by filing I-485) and may even lose your other possible benefits under EB-5 visa program. Advisably, consult your EB-5 attorney prior to taking any steps toward becoming an overstay through expired OPT.

You may not stay in the U.S. lawfully with a pending I-526 petition or apply for another EAD, based on a pending I-526 petition because I-526 does not allow for such benefits. One of the options for you is a timely enrollment in school before your OPT expires and to continue your education on F-1 status while you are waiting for a decision on your pending I-526 petition. You may also consider changing status to E-2 if you have eligible nationality. You should consult an immigration attorney to review possible options.

Your pending I-526 petition does not give you legal status to stay in the United States.

No you cannot. Only if I-485, pending with an approved I-526, can you stay.

You cannot stay in the U.S. once your OPT extension has expired unless you are able to transition to another valid non-immigrant U.S. visa status. The fact that you have a pending EB-5 investor petition on Form I-526 does not create any lawful status. You do not obtain a lawful status in the U.S. until your I-526 petition is approved and, assuming visa numbers are available and you are in lawful status, you file an application for adjustment of status on Form I-485. It is only then that you acquire a separate status. If you do not maintain a lawful non-immigrant status, you will lose eligibility to file your application for adjustment of status on Form I-485 and could become subject to a three-year or even a 10-year bar or prohibition from re-entering the United States if you accrue more than six months of unlawful presence in the United States for the three-year bar or more than one year of unlawful presence for purposes of the 10-year bar.

A pending I-526 petition does not give you authorization to stay or work in the U.S. You should look into other options for work authorized nonimmigrant visas (i.e. E-2) that you may change status to while your I-526 is pending.

If you overstay your F-1 OPT, under the new rules if enacted, you will be accruing unlawful presence. Once you have 180 days of unlawful presence, you barred for at least three years when you leave. You need to look at other visa options, such as an H-1B, or possibly even an E-2 if you have or can get the right nationality.

A pending I-526 does not provide you with a right to stay and/or work in the U.S. If your studies qualify for STEM OPT extension, that would be your next logical step. Otherwise, H-1B or F1. You may have other options depending on your specific circumstances or country of origin. You should consult with an attorney.

No, you cannot stay legally. You should contact an immigration lawyer immediately. If you overstay by too long, you cold get barred for either three or 10 years.

Once your OPT expires, you need to leave the U.S. even though you have a pending I-526. Filing an immigration petition itself does not grant you the right to overstay your status.

If your OPT is expiring, the only way you could stay is to enroll into another school and attend the school as I-20 indicates. Because there is no EAD allowed until after I-526 is approved and you could file the I-485, you cannot simply stay after OPT ends. Under the new enforcement actions announced by the USCIS, any stay beyond the legitimate F-1 status, including OPT, without proper enrolling and attending school that violates the duration of status will be considered unlawful presence. If you have accumulated more than 180 days of unlawful presence, you will have either a three-year bar or 10-year bar to be admitted into U.S. This means even if you have I-526 approved, you may not file I-485 to adjust if you are out of status. If you accumulated more than 180 days of unlawful presence, you cannot file and get the immigrant visa for three years.

No, you can only stay for the 60-day grace period. So if you want to remain longer, re-enroll in school, new I-20, etc.

Unfortunately, a pending I-526 application does not give you a lawful immigration status. You will need to maintain a non-immigrant status until the I-526 is approved if you wish to remain in the United States. Otherwise, you will need to return to your home country until the I-526 is approved and then apply for consular processing.

The question depends on whether you filed to adjust your status with the 526. And, if not, whether your priority date is current.

A pending I-526 does not grant any temporary status. You may consider enrolling in a continuous education program and changing your status back to an F-1 while you wait for an I-526 approval.