What you refer to as "non-clearcoat" paint is typically called "two-stage paint" because the paint is applied in two stages: a color coat, which dries to a dull finish, and a "clearcoat" that protects the color coat, has anti-UV components, and dries to the desired finish (usually glossy).
Single-stage paint is a color coat that dries to a desired finish -- usually glossy.
Most all newly made cars have two stage paint. There are some advantages to single stage paint, however. One thing I have always liked is that you can polish down to fresh (unoxidized and unmarred) paint. You do this by removing a small amount of the top of the coat. Of course, the top paint you remove is going to go somewhere and one of the places it goes is on to what ever you are using to apply the polish. So, it is normal and expected that the cloth you were using would turn black.
If your paint has any defects: oxidation, scratchs, etc. I suggest you continue to polish the car until you expose clean, fresh paint. Do a search to find the many times the good people on this site have explained how to use polishes and rubbing compounds.
When you have finished, you can apply Klasse, Zaino, or any other product of your choice. If you chose Zaino, Zaino makes a special protectant designed for single stage paint. If you use Zaino, you will first apply the base coat product (called Z1) which is used both for single and two-stage paints. Then you will use Z3, the gloss and protection coat, which is designed for single stage paints.
Welcome and good luck.
Excellent pics too by the way...
