@mjbomar - if you got the new Mac Mini M1 then you may have the best DVR platform available at this time per a comment from @tmm1 elsewhere in this Support Community.
Yes, you will be able to stream 3+ TVs at the same time as long as your internal / home network can handle it - gigabit is recommended.
You asked about not letting the HD go to sleep -- but I don't think there is an internal HardDrive -- from what I see all new Mac Mini M1 ship with SSDs not HD.
Here are the specs per Apple.