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At DigitalOcean, self-managed hosting is provided. This means you setup the installation, from the Web Server to the Magento store you wish to run. You are provided with a droplet (ie virtualized machine) and credentials for the root user (unless an SSH key is provided). Because of this, a lot of your questions depend on how you setup the droplet and make it work for you.
You can always resize to a bigger droplet if your store grows and needs more resources at its disposal. You can find guides on resizing and downsizing via this article on resizing and this article on downsizing.
While DigitalOcean provides a backup service you can utilize (for an additional cost), it would be run on a weekly basis, so you might wish to make a custom script or cron job to handle making daily backups of your database.
None of the services you make on the droplet would be behind a load balancer unless you set one up. You could make one using one of the many DigitalOcean articles covering load balancing if you wished, or utilize our floating IPs feature to help in the process.
You can certainly use Git if you so wish. It all depends on your setup. You can find many articles on using Git via these articles.
You can view the full list of packages and prices here.
Hope it helps, and happy coding!