Yes, our VPS support databases and most of the languages. You could see more features for our VPS from here: https://www.dynadot.com/hosting/vps.html
For the second question, if the domain is connected with the hosting correctly, it should be good. There might be some propagation issue when you move a domain to another hosting.
And please notice that the VPS hosting is an unmanaged service. Users will be expected to manage their own software installations and troubleshoot issues with their VPS on their own.
We offer multiple free templates with Sentora, zPanel, and WordPress pre-installed, cpanel is not included unfortunately. However, if you want to use cPanel with our VPS Hosting, you can choose to add it. Our VPS Hosting offers users all the benefits of a dedicated server without the cost and gives users the ability to install any control panel they want, including cPanel.
If you want to use cPanel with our VPS Hosting, please be aware that cPanel is not free and will require you to purchase a license: https://store.cpanel.net/cart/. We may add more in future but now only one package is available: https://www.dynadot.com/hosting/vps.html.