I found a retailer in UK and he said that the pro kit, lowers the car but does not add any stiffness and if I want to do that, I have to buy shocks as well.
Is this true or not? because as I understood from your message, shocks are not needed. maybe this guy wants to sell only?
Unfortunately the word "stiffness" is used both for dampers and springs even though the word has a different meaning for these two components. In the case of dampers it generally means how resistant the damper is to movement; i.e. the more the damping capability, the "stiffer" the damper. In basic terms, a damper provides resistance to suspension movement (not weight) and the more rapid the movement the greater the resistance (stiffness) .
Springs, on the other DO provide resistance to weight; i.e they hold the car up. They respond at a rate often measured in pounds per inch of compression. "Stiffer" springs have a higher "pounds per inch" rating. But they don't react to the rate of movement like dampers do.
Springs and dampers usually work together and when carefully matched and optimized they provide optimum handling for a given situation. There is, of course, a trade off between "stiffness" and ride quality.
Fitting dampers without springs would have your car sitting on the suspension stops with horrible handling. Likewise, fitting springs without dampers would give you the right ride height, but the car would bounce all over the place. You need both or course.
The springs in question are shorter than standard which is the primary reason they lower the static ride height. They are also "stiffer"; i.e. they require more force to compress them than the standard springs require. That means the ride is less complaint but you'll have less body roll and overall better handling. In spite of your car being lower, it will be less likely to bottom out in road dips because the Eibach springs are indeed "stiffer", contrary to what your supplier says.
Ideally, you would also fit improved dampers too, but as mentioned earlier, they are quite expensive. If you're either on a budget or simply unwilling to spend that kind of money, you can get a nice improvement in handling with the springs alone. I can testify to that because that's what I did and I do not feel the need for spending a wad of cash on better dampers. I do spirited driving on ordinary roads, not flat out driving on a track.