Why did the dishes become darker after the first use?

They change colour and become darker if you do not wash them before the first use. It is due to the fact that during a production process, they are covered with a special protection fluid, which you need to wash off before the first use.

58 How can I find out whether or not the pan with a normal bottom is heated up, without placing a lid on it?

You should perform the test of a water drop. Pour a few drops of water onto the pan, and if the water starts to jump around, it means that the pan is heated up and ready to fry on.