How can I apply for EB-5 as an F-1 visa holder without leaving the United States?

Yes, that is doable. I would elect consular processing to show the continued intent to return overseas. This can be changed to an adjustment later if you are still in status by filing the I-485 here.

Yes, you can apply for an EB-5 while you are still in school. You can continue to maintain your F-1 student status while the case is pending. The only think I would worry about a little bit is, if your visa in your passport expires before you finish school and your Optional Practical Training, you will need to get it renewed at a consulate, and they may not want to renew it if you are applying for a green card. So, you might be stuck in the U.S. for a while your case is pending.

If you were not born in China or Vietnam, and assuming there is no EB-5 immigrant visa number retrogression for other countries, you can file an adjustment of status, if you are still physically present in the United States, and in valid F-1 (or other nonimmigrant) status at the time your I-526 petition is approved.

You will need to maintain your F-1 student status for at least the two-three years that the USCIAS presently takes to adjudicate the petition. The filing of the I-526 does not help you stay while its pending.

Yes, you can file I-526 while in F1 status.

Yes, you can apply for the EB-5 and generally do not need to leave the U.S. as you can adjust status when its approved as long as you are still on an F-1 visa.

You may file I-485 to adjust your status after your I-526 approval if: 1) an immigrant visa is available to you (that is, you are not subject to any country-specific visa backlog); and 2) you are in the U.S. under a valid nonimmigrant status. So, theoretically, you can wait in the U.S. if you meet the above conditions.

Yes.