Not in the UK
I don't know about every state, but in most, no. You can get just a motorcycle license.
Yes. If you possess a drivers licence, you'll have to get a motorcycle endorsement added to it in order to be able to operate a motorcycle.
No you don't need to get a full car driving licence to get a motorcycle license, you can ride a 50cc moped (whether this is styled like a motorbike or scooter doesn't matter) at the age of 16 with...
It matters where you are.
you would need a m-class endorsement to ride a motorcycle