VPS Charged hourly even with monthly payment?

There’s no such thing as monthly billing.

Your droplet is charged as long as it exists, and stops being charged when you delete it.

There’s no restrictions to what you can do on the box other than what’s forbidden by the DigitalOcean Terms of Services.

All droplets are charged at their hourly rate with that cost capped in each calendar month at their monthly rate, so a 512MB droplet that exists for 1 hour would incur $0.0074 in charges (if you destroyed it after one hour the total would be rounded to $0.01). If this droplet exists for the whole month you would see the charges on your account go up until they hit $5 which would happen near the end of the month.

You are billed for all droplets on your account. Resources on the hypervisor remain allocated to your droplet when it is powered off. If you need to save a droplet for later you can always create a snapshot of the droplet from the control panel before destroying it. This way, when you are ready to work with it again you can simply create a clone of your original droplet by using your snapshot image instead of a stock OS or application image.