Look in the Field Menu and select those fields. For me, the key shortcuts are C-c C-f C-c (message-goto-cc) for CC and C-c C-f C-b (message-goto-bcc) for BCC. These will add those fields.
Alternatively, I think you can just type them in yourself in the header, e.g. after the To: line, press enter, type Cc: and a space then add the email address you want.
So is it possible to use message mode without a header?
Would narrowing to the body work in your use case? See (info "(emacs) Narrowing"). For example, you could C-c C-b (message-goto-body), C-SPC (set-mark-command), M-> (end-of-buffer), C-x n n (narrow-to-region). To undo the narrowing, you could C-x n w (widen).
Here's a command that does ...