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As we say in Germany: there's no such thing as dumb questions. Only dumb answers. So, please, if you have any questions, just ask them.
I'm trying to get the Harmony Ultimate to Power Up the MAC... How?
A Mac can only be powered on with the power button on its case. It can't be powered on via Bluetooth, USB or IR.
You can, however, wake your Mac mini via Bluetooth, USB and IR, though.
Mac minis are pretty power efficient these days. The latest Mac mini from 2014 consumes just 0.75W when sleeping (0.29W when turned off), so you don't save much energy by powering it off. (Source: https://www.apple.com/environment/reports/ )
Is it possible to assign a single button on the Harmony remote to power down the MAC?
Yes. Go to Prefs > Mapping > Global mapping and select "Miscellaneous > [power action of your choice]" for the button you want to dedicate to this.
Cheers,
Felix