The loan agreement lists the terms under which a loan is given. The bank is the lender, and any borrowing entity--individual, partnership, company--is the borrower. The loan agreement covers many of the same terms and conditions as a promissory note, although it is longer and more complicated.
The subsidiaries remain private. They are private subsidiaries of a public company. Think about it: if a subsidiary went public, that would mean that its shares were being offered to the public, instead of all being owned by the parent company, and so it would no longer be a subsidiary.
What is a 'Holding Company'. A holding company is a parent corporation, limited liability company or limited partnership that owns enough voting stock in another company to control its policies and management.