When you take a snapshot of a droplet, everything on the local file system of that droplet is backed up in a snapshot. So all files, configurations, installed items, etc are backed up.

As the comment suggests, if you create a new droplet you will get a new IP so you will have to update your DNS accordingly.

If instead you “restore” a droplet from a snapshot, the IP will be preserved and you will not need to make any DNS changes.