How do I restore an Amazon EC2 instance from a backup?

Question

Amazon Web Services

There is a site hosted on an already created and running Amazon EC2 instance. Elastic IPs are not used.
How to correctly backup an instance and how can I restore an instance in the shortest time without losing the existing IP of the site (instance)?
I conducted an experiment - if you take a snapshot, create an image from it and connect it to an existing instance (as recommended in the documentation) - you have to turn off the instance, which leads to the loss of the existing IP.
Elastic IP can be enabled, but it does not allow you to select an existing IP, but offers to generate a new one.
I want to avoid the need to change the IP of the site, access to the DNS records of the site is limited. Yes, and it's nonsense to change the site's IP every time you restore from a backup.
I've looked all over the documentation but haven't found a way to restore a backup without shutting down the instance.

Answer 1

The IP will always be dynamic until you buy it. Use DDNS for binding and don't bother yourself with non-existent problems.

Answer 2

You need to get an elastic IP once and use
it if you don’t restart it, then back up internally
duplicity rsnapshot
bakula
and other backup systems