how do I send a mail message to multiple recipients and hide their addresses?

The hamburger button is how you enable the BCC field, yes.

I'm assuming that this is an OS X question given where it's posted, though your posting footer lists only iOS. Create a new message. Add all recipients as BCC'd entries. If you don't have the BCC field showing up when you create a new message in Mail, then use the "hamburger menu button" settings to add its display. If this was an iOS question posted in the OS X forum, then start the message in iOS as you would, and press the BCC text in the message header to open up the BCC field, and enter the users there. In either case, test the output before sending your messages, to confirm it's all working as you expect.

A mail server is a common alternative, GNU Mailman or Listserv or any of various commercial offerings — the groups support has some limits in features and flexibility.

If your question is how to hide members of a group of e-mail recipients then do this from the Apple Knowledge Base....

To prevent individual email addresses from being shown when you send messages to groups, choose Mail > Preferences, click Composing, then deselect “When sending to a group, show all member addresses.”

Hutchoo wrote:

Great that worked.
Groups now get the message individually, but only if you put the group name in the Bcc box, duh.

How can I set up mail so the incoming messages populate the screen when I click on the mail icon (like they used to in Mountain Lion)????

If I understand what's being requested, then either Mail > Preferences > Viewing > check Use Classic Layout, or — if the newer three column view is what you're after — see whether the items on the bottom of the Mail > View menu get you where you want.