Calling your Cloud Function via an URL and sending back a response
By doing exports.firstTest = functions.database.ref('first').onWrite()
you trigger your firstTest
Cloud Function when data is created, updated, or deleted in the Realtime Database. It is called a background trigger, see https://firebase.google.com/docs/functions/database-events?authuser=0
With this trigger, everything happens in the back-end and you do not have access to a Request (or a Response) object. The Cloud Function doesn't have any notion of a front-end: for example it can be triggered by another back-end process that writes to the database. If you want to detect, in your front-end, the result of the Cloud Function (for example the creation of a new node) you would have to set a listener to listen to this new node location.
If you want to call your function through an HTTP request (possibly from your front-end, or from another "API consumer") and receive a response to the HTTP Request, you need to use another type of Cloud Function, the HTTP Cloud Function, see https://firebase.google.com/docs/functions/http-events. See also the other type of Cloud Function that you can call directly: the Callable Cloud Functions.
Finally, note that:
Calling, from your Cloud Function, an external URL
If you want, from a Cloud Function, to call an external URL (the Slack webhook mentioned in your question, for example) you need to use a library like request-promise
(https://github.com/request/request-promise).
See How to fetch a URL with Google Cloud functions? request? or Google Cloud functions call URL hosted on Google App Engine for some examples
Important: Note that you need to be on the "Flame" or "Blaze" pricing plan.
As a matter of fact, the free "Spark" plan "allows outbound network requests only to Google-owned services". See https://firebase.google.com/pricing/ (hover your mouse on the question mark situated after the "Cloud Functions" title)