For the answer to your first question refer to this answer - https://stackoverflow.com/a/65447848/4691279
For your second question - you can use command like docker ps --filter "name=<<<YOUR_CONTAINER_NAME>>>"
to check whether a particular container is running or not.
If Docker and Container both are running then you will get output like below:
$ docker ps --filter "name=nostalgic_stallman"
CONTAINER ID IMAGE COMMAND CREATED STATUS PORTS NAMES
9b6247364a03 busybox "top" 2 minutes ago Up 2 minutes nostalgic_stallman
If Docker is not running then you will get an error message saying docker daemon is not running.
If Docker running but Container is not running then you will not get the container name in the output of this command.