Yes, you may apply for an EB-5 visa while under an F-1 status. In terms of the funds, your father may gift you the funds and it must be documented. Also your father must provide documentation as to the source of the funds gifted to you.
You may wish to treat the funds from your father as a gift. These gifted funds can be classified as your personal EB-5 funds invested in the EB-5 project. Your father will have to provide the authentication of the source of personal investment funds. Whether you are in legal F-1 status in the U.S. or not, you may file an investors I-526 petition.