Most mobility scooters have a ranger of between 15 miles to 30 miles that they can go before a recharge is needed.
The actual distance that the mobility scooter can go before depleting the battery depends on the size of the mobility scooter and the battery or batteries that they can contain.
Also you must have the mobility scooters battery fully charged for it to go the farthest distance it can go as you'll be able to go less miles with a lower charge in the battery.
But for the smaller mobility scooters that have a fully charged battery they can go or should go at least 15 miles on a full charge.
The larger scooters can sometimes go 20 to 30 miles.
Mobility scooters do not need to be registered like motor vehicles do.
You can usually legally ride your mobility scooter down the road even without needing to register it as long as you're driving the mobility scooter down the road safely.
Mobility scooters are allowed to be driven on pavements in most places.
However check with your local laws as some places may not allow the mobility scooter to be drove on public roadways especially the busier roads.
I've seen several people driving their mobility scooters on the roads and they have not gotten into trouble for it nor stopped and they've passed police who said nothing to them.
As long as you're not drinking and driving the mobility scooter you should be just fine driving the mobility scooter on the pavement.
Also make sure you're watching traffic and other vehicles should move over to get around you as well but you need to be aware of any oncoming traffic.
Ride the mobility scooter down the pavement in the direction where you can see the vehicles coming towards you.