No.
According to an email between myself and the Texas Department of Motorcycle Safety (dated October 2010): "A passenger on a motorcycle must be at least 5 years old. Texas Transportation code Sec....
No it is not. A vehicle is usually a 4 wheeled vehicle. Motorcycle is in its "own" category
Not safely and not legally.
Yes it is allowed in your baggage, both checked and carry-on. Though I will advise you to wrap it well to avoid breakage.