Eli5 question about supercritical steam turbines

Does the water stay in a supercritical state within the steam generator, the turbine and the plumbing in between?

What happens to the supercritical fluid as it passes through the turbine? Does it drop in temperature? Pressure? both?

Is the improvement in efficiency over superheated steam that you can have a larger pressure drop over the turbine without phase change?

How do you keep the supercritical fluid from eating the turbine, plumbing, etc.?

I just today heard the terms sub, super and ultracritical coal fired power plants with regard to China and my curiousity was peaked. Are any of these coal plants using CO2 supercritical turbines?