Docker image inside AWS AMI image

Question

I have question, Say you have an EC2 instance running with some of Docker containers in it.

1) Can I create a AMI with that Docker images? 2) If AMI created, how the docker images are downloaded (from within AMI or from the Docker hub)? 3) Best strategy , Docker should call AMI or AMI should call Docker? Provide me some pointers to get more details,

Thanks in advance