How to check if the docker engine and a docker container are running?

Question

In a script, I need to check:

a) Is the docker engine running?
b) Given a container name, is that docker container running?

[the initial wording of this

Answer 1

If the underlying goal is "How can I start a container when Docker starts?"

We can use Docker's restart policy

To add a restart policy to an existing container:

Docker: Add a restart policy to a container that was already created

Example:

docker update --restart=always