Connecting magic keyboard to the old Mac

I'm afraid not, the oldest Mac Mini listed compatibility under is from 2014, plus you will need macOS 11.3 or later.

Magic Keyboard - US English - Apple

Same for the Magic Mouse, and your Mac has to have OS X 10.11 or later installed:

Magic Mouse - White Multi-Touch Surface - Apple

Look on E-Bay for the older wired Apple aluminum keyboard, or a wireless keyboard compatible with Bluetooth 2.0+EDR.