How could executive order on immigration affect I-551 renewal?

No, EB-5 and green card holders are exempt from the new bans.

The order did not affect anything going on inside the U.S., fortunately. Just folks needing the Consulate/Embassy abroad. Also, EB-5 was exempted.

No. Executive order is just an executive order. It can change the manner to implement the law, not the law itself. The two-year conditional status will be extended if the expiration is not caused by the fault of the residents and it is the law. No executive order is permitted by the constitution to change the law.

The Executive Order does not affect EB-5.

It should not since you are a permanent resident and you are in the U.S.

It should not, except it could cause a delay in the issuance of the same due to the furloughing of employees and delays in in-person interviews.

The current executive order does not affect EB-5 visas and certainly not conditional permanent residents in the U.S. at this time. INFOPASS is more or less a thing of the past, though.

The executive order does not apply to persons in the United States or to lawful permanent residents. The problem with obtaining your I-551 extension stamp is not the executive order, but a dysfunctional USCIS that is not scheduling InfoPass appointments except for emergencies or health care workers. An expiring I-551 stamp, by itself, does not seem to qualify as an "emergency" according to USCIS. I am advising my clients to wait until more USCIS offices open for in-person, public services, hopefully later this month. There is also the option to sue USCIS in the case of an employee who is about to lose his or her job because of a lack of proof of continuing conditional permanent residency status.

In a word: No.

No. The problem for people who need I-551 stamps is Infopass appointments are available in many cities only to those with a documented urgent situation.

The executive proclamation states that it does not include people who are in the U.S. nor does it include green card holders. As such it does not appear relevant to you.