The power required will depend on the terrain. Scooters will need to climb quite a slope for a short distance.100 or 200W may do on a good surface.
1. 24V is better than 12V because the current is half so there are fewer resistance losses. Trams use about 700V, now that is a thing to aim for.
2. Ah is the battery capacity so a 20Ah battery can give 1A for 20 hours or 2A for 10 hours. It is amps * hours NOT amps/hour.
The motor shown does appear to have no rear bearing and will need a matching gearbox to work.