If I take a backup using the snapshot, will it include the droplet + the domain on top of it + the lets encrypt cert?
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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.
Sure, but if you deploy the snapshot to another droplet with a different ip you will have to point your domain at the new ip.