When I connect the dongle to the Android mini PC it's obviously not going to be able to function as an iBeacon(and by iBeacon here I mean the actual hub that enables nearby devices to communicate) right away. What do I have to do to turn it into an iBeacon? Is there some library I can easily install? Or do I have to do something crazy like reverse engineer the "iBeacon protocol"?
Unfortunately, Android devices cannot act as iBeacons without heavy low-level modifications. See here.
The answer above is for Android phones, but the same obstacles apply to a mini PC. Connecting an external Bluetooth dongle is just the first challenge. You would then need to overcome these hurdles:
This is probably way more than you want to bite off!