Paul, I believe many of the things you are asking for are already available to you.
Ability to change status - You can do this in Settings (online / offline)
Ability to message ( in an invite ) - Does not exist yet. Would be very useful.
Ability to see and invite when friends are green - You can do this when setting up a multi-player game. Click INVITE.
Ability to invite non friends that are green ( random ) - You can do this when setting up a multi-player game. Click ANYONE. Or click INVITE and type in the non-friend's name.
Ability in the lobby to type in suggested players - Use the CHAT feature in the lobby to do this.
Ability to have time to respond to an invite - After the white invite box disappears, just go to the main screen and look at the bottom for Invites (1)
In this new system . I don't even know how an invite is visible , where to look or find it .
Just go to the main screen and look at the bottom for Invites (1)
While I am on and green . I would like to be available to be invited for random multiplayer rounds . How does one make themselves available for that ?
Go to the GAME MODES, select the multi-player game type you want, then click the blue JOIN A GAME button.
Hope this helps.