Can You Legally Ride One Of Those Mini Motorbikes On The Road?

Yes, if you remember that is a motor vehicle like any other.  That means, regardless of it's small size, that a mini motorbike comes under the Road Traffic Act.  It needs to be taxed and licensed, like any other motor vehicle.  It must have appropriate safety accessories (like working lights), and is subject to an MOT.

The driver of a mini-moto needs to be at least 17 and must have a valid and appropriate driving license.  They must be insured and wearing a crash helmet.

Mini-motos can be ridden legally on privately owned land with fewer requirements, but only if the landowner has given permission.  And it can't be done if it causes nuisance, such as excess noise to neighbours. The police can seize and crush a mini-moto if the rider is uninsured or unlicensed, or if is otherwise causing nuisance.

Someone convicted of an offence involving a mini-moto may well get an endorsement on their licence. If the rider does not have a license (a child, for instance), then the endorsement may be delayed until they are of age.  In effect, they may be delayed in terms of when they can legally get a license.