Yes, you can get one at 14 years old.
You don;t need a license if your moped has 49cc's or less. Anything over 50cc's and you need a license.
If they are lawful to be operated on the public streets and roadways, yes.
Only if it is over 50 cc.
I talked to a guy at a bicycle shop and he said you have to be 16, just a regular drivers license (no motorcycle or anything like that), insurance on the moped, and the moped must have pedals