Think of the server/VPS as just a computer in another place. You use Windows RDP - a built in program on your PC - that lets you connect to the server/VPS exactly like you'd use your normal computer.
You don't need any specific server operating system, just use the one you think will work best for your purposes. i.e. it's new, you know how to use it, and ideally light on ram/cpu usage.
Yes, a Virtual Private Server. Fancy way of saying you access it virtually and it's private i.e. set up for you. Imagine you just had a separate computer at home you could install MP on, but to save time you just had one screen to access both and you could switch between the two computers.
cPanel is only if you want to have webhosting and have cPanel to manage it. If you aren't using this for web hosting - only MassPlanner - then don't worry, you don't need it.
If I were you I'd select an operating system you know how to use like Windows 10. Windows Server 2016 is pretty much Windows 10 anyway with slight layout changes. You can buy a key, or you can do what most people do and just use it anyway without a key, you'll just get Windows bugging you to buy a key after a few months.