What are the obstacles for immigrants who want to stay in the United States while waiting for their Adjustment of Status?

If you are already here in the U.S. under some lawful nonimmigrant (temporary) status, you must maintain lawful status until you can file for adjustment of status (that is, apply for the green card). You CANNOT make an entry with only an intent to adjust status.

Yes, while your adjustment of status is filed/pending, you are authorized to remain in the U.S. You should also simultaneously file for a work permit and advance parole so that you can work and travel outside the U.S. during this time.

As a Venezuelan citizen, if you have been lawfully admitted into the U.S., you can wait until your EB-5 Investor Petition on Form I-526 is approved; if in lawful status or otherwise eligible, you are then eligible to apply for Adjustment of Status on Form I-485. In order to do so, you must maintain your temporary status and file for extensions on a timely basis. Being from Venezuela, if you do not already have a visitor visa and if you have not already been admitted as a visitor, it may be difficult. Applying for a B-2/B-2 Visitor visa after you have filed your I-526 petition, which would have to be disclosed, would make it virtually impossible to obtain a visitor visa.

If you have filed the form I-485-Application to Adjust Status and you are waiting for the decision, then you are in lawful status. Of course, this is provided that you qualified to adjust status in the United States.

You must remain in lawful status while you wait for your EB-5 to be adjudicated. You should immediately meet with your Investment Immigration Attorney and determine the strategy that will help you meet your goals.

You may be able to stay in the U.S. after you file an EB-5 petition only if you have a non-immigrant visa that allows you to stay in the U.S. during the time your application is pending. Otherwise, you will need to leave after you file your petition and then wait outside the U.S. until it is approved.

Merely filing for EB-5 status does not give you the right to stay in the U.S. while your case is pending. To stay here, you must have some other immigration status for the nearly 2-3 years it will take to process your EB-5 case. E.g., Student status; H-1B; E Treaty Trader or Investor status; L-1; etc. You should consult your immigration lawyer about this, as the penalties are severe if you do not do it right.

You can remain only if you have a valid nonimmigrant status.

You have to be in status and not have engaged in unauthorized employment in order to adjust status in the U.S. Since the I-526 petition can take about 21 months to adjudicate, you have to be able to remain in valid status during all of this time. If you plan to study, a student visa may be an option. Otherwise, maybe a temporary work visa might be authorized. It is not smart to try and do this on a visitors visa. If you are in valid status in the U.S., you might then be able to stay while the adjustment application is pending. 3-4 months after filing the adjustment, you should be approved for a travel and work permit.

If you are attending school under the valid F-1 visa, you could stay as long as you are attending school. If you entered on a visitor visa (B1/B2) with 6 months duration, there is virtually no way for you to extend your stay long enough to go through the EB-5 process, as it is now taking nearly 20 months for I-526 adjudication.

If you wish to stay in the United States while your I-526 petition is pending, you need to maintain an underlying immigration status in the United States to be able to adjust status to that of a conditional permanent resident status, such as an F-1 student visa or a work visa for example. Otherwise, you need to wait abroad for I-526 Petition to be approved and then consular process for an immigrant visa abroad and arrive in the U.S. as a conditional permanent resident.