What happens with data in Ephemeral storage when I stop EBS backed instances?
AWS makes a snapshot and store it in EBS - not losing data?
AWS makes a snapshot and store it in S3 - not losing data?
AWS makes a snapshot and store it in EBS - losing data?
AWS makes a snapshot and store it in S3 - losing data?
https://stackoverflow.com/questions/30627084/what-happens-with-data-when-i-stop-ebs-backed-instances
https://stackoverflow.com/questions/11566223/what-data-is-stored-in-ephemeral-storage-of-amazon-ec2-instance
If you are not sure what type of volume you have, look under EC2->Elastic Block Store->Volumes in your AWS console and if your AMI root volume is listed there then you are safe. Also, if you go to EC2->Instances and then look under column "Root device type" of your instance and if it says "ebs", then you don't have to worry about data on your root device.
http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/RootDeviceStorage.html
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/ec2-instances-and-amis.html
To keep important data safe, you should use a replication strategy across multiple instances, or store your persistent data in Amazon S3 or Amazon EBS volumes.
SO if you are using Amazon S3 or Amazon EBS volumes , you will not lose data when stop the instances.
About the fee
You are not charged for additional instance usage while the instance is in a stopped state
All of the associated Amazon EBS usage of your instance, including root device usage, is billed using typical Amazon EBS prices.
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/RootDeviceStorage.html
You can choose between AMIs backed by Amazon EC2 instance store and AMIs backed by Amazon EBS. We recommend that you use AMIs backed by Amazon EBS, because they launch faster and use persistent storage.
Terminating an instance?
Of course, all data will be deleted by aws.