Answer 1

If you're going to be making a web-based game, you can't build it with JUST JavaScript. JS is a client-side language, meaning it has to run while the window is open.
Clicker Heroes, for example, when you buy certain upgrades can click for you even when you close the game. They have to use a server-side language such as SQL to automatically add those points.

Answer 2

I'm actually not sure about this, since I don't know a thing about node.js. Take my suggestion with a grain of salt.
I did some research, and I do believe that Node would be a nice candidate for the language you are looking for. However, I think you should do some more digging around the internet to see if it would really work. Unless, of course, you already know a lot about Node.