Free/busy is a determination of whether there is a calendar event in a given time slot. Free designates time slots without events and busy designates time slots that are taken up in a person's calendar. Any account within Office 365 will have the ability to view free/busy information against any other Office 365 account.
Full Mailbox Permissions
In Office 365, this permission allows a delegate to create or modify emails, calendar items, and contacts. To allow a delegate to send email from the user's mailbox, you still have to assign the delegate the Send As or the Send on Behalf Of permission.
For information on how to manage full mailbox permissions for an account, click here.