1) While a CB user is creating an invite to send, is there a way to display the header and footer? I would like the "inviter" to see what the invitation email will contain in its entirety.
This was removed by popular request. To add it back you'll need to edit the CB Invites template to include it. Please see the below template file.
components/com_comprofiler/plugin/user/plug_cbinvites/templates/default/invite_edit.php
2) The purpose of the invitation code.
It lets them accept an invite while using an email address different from the one they received the invite to.
Is a new one generated each time an invite is issued? Is this how CB tracks if an invitation was accepted?
Yes.
If the code is not entered during registration, is the registration decined?
Only if you make the field "Required". Otherwise, no.