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A droplet is a virtual private server. You are not sharing it with anyone. (You’re actually sharing hardware - there are a bunch of droplets running on a single piece of hardware.) You configure it to your liking, and you maintain it. You get access to whatever you install on it. If you want a control panel, you install it. There are several options. I’m using Virtualmin on one droplet acting as a mail server and running Apache, and no control panel on another droplet running Nginx and MySQL.
See https://www.digitalocean.com/pricing/ for pricing information.