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

Run:

docker version

If docker is running you will see:

Client: Docker Engine - Community
 Version:           ...
 [omitted]

Server: Docker Engine - Community
 Engine:
  Version:          ...
 [omitted]

If docker is not running you will see:

Client: Docker Engine - Community
 Version:           ...
 [omitted]

Error response from daemon: Bad response from Docker engine