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.
In the law of corporations, a corporation or company owned by another corporation that controls at least a majority of the shares. A subsidiary corporation or company is one in which another, generally larger, corporation, known as the parent corporation, owns all or at least a majority of the shares. As the owner of the subsidiary, the parent corporation may control the activities of the subsidiary.