Thank you for your question.
First of all, you need to understand that you cannot conduct any work for remuneration in connection with this venture while you are on an F1 visa. That means you cannot act in any way or perform any duties for the LLC without a work visa.
In order to get an ITIN you must submit a Form W-7 http://www.irs.gov/pub/irs-pdf/fw7.pdf
Unless you hire an agent who will act for you in registering the LLC, then the initial member who registers the LLC must have an ITIN.
When incorporating an LLC, the actual ownership of the LLC is decided by a private agreement between the members. The members of the LLC are not actually listed on the articles of incorporation.
To legitimately operate a US business, it is helpful to open a US account and to have a US credit card for the business. However, it is not necessarily required. For example, you can accept payment via PayPal, which does not require a US business account.
You say that you are going to use a permanent resident as the manager. Since the manager has residency, the manager already has the right to work in the US. Accordingly, you could instruct the manager to open up the LLC after signing an agreement with you and the rest of the members of the to be formed LLC which grants
you and the other members ownership, and maintains him as only a manager with no ownership. The he would have to fill out the following form: http://corp.delaware.gov/llcform09.pdf
This gets around you having to get an ITIN and prevents you from being listed on any document filed with the state which could lead Immigration to believe you were conducting work without a visa.
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