Yes you can, but you need a motorcycle license.
In california
To ride a 150cc scooter in Illinois you need a class L license. To ride anything greater than a 150cc displacement a class M license is required in Illinois.
no
Please check the Motorcycle Manual (related link).
Yes, also plates, license, and registration.
no. must be inspected/tiltled and registered, but do not need a license.
yes you need a mc endorsement to ride any motorcycle regardless of cc size.
yes
yes its possible for a 14 to ride a motor scooter. minor may not ride on side walks or walk ways.
No. Not a "scooter". A goped, yes, so long as you were a bike helmet, ride on streets with no more than a posted 25mph speed limit or on bike paths. A 50cc moped requires a m2 license and a "scooter" under 150cc's can't be taken on the highway and needs a m1 license. Search for California Vehicle Code (CVC) and you can read all about it, and print it up to wave in a cops face if they give you problems. -Ryan
yes and make sure before you buy it that it is legal to put on the road, some scooters are not allowed in NJ.
Depending on what particular state do you live. Here in California, You can ride a motorcycle w/ a learner's permit ONLY on days and NO passengers and only on your local roads and No freeways.