Can discourse do this? Putting users into groups, mass messaging those users?

[ondrej]

@snow

Place individuals into “user groups” or roles that would have permission to private categories. i.e. Tech support staff gets access to Tech support group, but no one else does.

Yes, you can make a group (private perhaps) then when you make a category, you can change security settings so only your group can create/reply/see

@snow

Can the administrators of private groups send Direct Messages/PM to people in that group? i.e. Administrator send all members of the Tech support group a heads up that a system is down.

Again, yes they can. Anyone can. Just go to the group and press message.

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(Not sure about your last question. I will add pictures later.)

Hope this helps you.