Make sure you enabled the plugin in the project settings. In the menu go to Project -> Project Settings. This opens the project settings dialog. There select the Plugins tab and tick the Enable checkbox near the Godot State Charts plugin.
I'm afraid not. While it technically would be totally possible to do so, I don't have the bandwidth for maintaining two versions of the library. I prefer to focus on the latest version of Godot, which is currently 4.
Yes, you can. The library is written in GDScript, but it provides a wrapper API for C# as well. Please check the manual for more information.