I have never owned a moped, but I have owned several Harleys.  
That's pretty cool, mopeds seem really convenient because they have less stringent licensing requirements than cars or regular motorcycles.
Not where I live.  If you ride anything motorized with two wheels, you must have a motorcycle endorsement on your license.
That's unfortunate, around here I don't think you need a license at all since they only travel as fast as a bicycle on public roads typically.
Most mopeds I have seen will travel 55-65mph.  Mopeds are very convenient for large cities, but I would be scared to ride one so slow in rural areas where the speed limit is over 65mph.
I'd be scared of riding such a small device so quickly, especially when you're unprotected, I can't imagine going 55 on a bicycle, that's crazy.
There are moped that are larger than bicycles.  They make some mopeds very sturdy with 100cc motors.
directly between the saddle and the head tube. Some resemble motorized bicycles. Most are similar to a regular motorcycle but with pedals and a crankset that may be used with or instead of motor drive. Although mopeds usually have two wheels, some jurisdictions classify low-powered three- or (rarely) four-wheeled vehicles as a moped.
In some countries a moped can be any motorcycle with an engine capacity below 50cc.
Etymology.
The word "moped" was coined by the Swedish journalist Harald Nielsen in 1952
Moped
A moped ( ) is a type of small motorcycle with bicycle pedals, generally having a less stringent licensing requirement than full motorcycles or automobiles. Mopeds typically travel only a bit faster than bicycles on public roads, and possess both a motorcycle engine and pedals for propulsion. Mopeds are distinguished from scooters in that latter tends to be more powerful and subject to more regulation.
Some mopeds have a step-through frame design, while others have motorcycle frame designs, including a backbone and a raised fuel tank, mounted