Messages are an intra-class communication tool exists entirely within the confines of the course. Messages are composed in an html (rich text) editor, so a variety of message styles are available. You may attach files. In order for both you, and your students to receive notifications of new messages when logging into Bb Learn, you should add a My Messages module to your course notifications page. Read the tutorial.
Unfortunately you cannot send Messages to particular Bb Learn course Groups.
The Bb Learn email system functions solely to send emails, not to receive them. All emails sent from BB Learn will go directly to the recipient's Wildcat email inbox, or whatever address the recipient has set that account to forward to. Student replies to emails sent by instructors will go to the instructor's CSU, Chico Exchange account. Once an email had been sent, it will never re-enter the BB Learn system.
There is no "sent" folder in BB Learn, but email senders will receive a carbon copy of all emails sent. Additionally, the sender can select the check box to have the carbon copy include the list of recipients, this is called "return receipt". The check box can be found to the bottom left of the message window:
Read the tutorial: How to add the Email or Messages tool link to the course menu