How can I manage my EB-5 business with a visitor visa while waiting for my case to be approved?

No, you cannot be operating the planned business with the visiting visa. Either "supervising" the business or "management of the business" is still considered to be working in the U.S., which is not allowable under your visiting visa.

You can set up but not run the business on a B1 business visitor visa, which is not ordinarily approved for 180-day admissions but often is limited to 30 days. You would be advised to set up the business on an E-2 visa, if eligible, or on another visa category, such as an L-1 if you qualify.

You do have the right to extend your 180-day stay once in the U.S., but it is important that you are not considered working there.

You can visit your business, conduct further due diligence, and generally see how things are going, but your supervising/work abilities are limited with a B2 visa. For example, you cannot be paid a salary or any money from the business while you are over there.

You have the right idea with a U.S. manager. You cannot be engaged in the management of the business at all though.

You cannot be involved in any employment activity, which includes any form of management during the period of adjudication of both the EB-5 I-526 petition and the application for conditional permanent residency.

A B1/2 visa holder must remain compliant with B1/2 terms. Specifically, no employment is allowed. Periodic visits to conduct oversight are OK as long as you are not actively participating in management or day-to-day activities of the business. CBP has ample resources on this topic and your attorney can evaluate specific activities you have in mind.

You can only act as an investor and not as an operator/manager. You can not operate the business at this stage since you do not have employment authorization.