Виктор: блин все же есть прямо в их основном факе
Am I charged while my droplet is in a powered-off state?
Yes. Your diskspace, CPU, RAM, and IP address are all reserved while your droplet is powered off. If you want to save a droplet for future use take a snapshot of it and then destroy it. You'll be able to create a new droplet from the snapshot image anytime to bring it back online.
Do I have to pay the cost of the server every time I create a new one?
No — you only need to pay for 1 hour of usage. Spinning up a new 512MB server just to test something for a couple of minutes will only cost you $0.0074