How to disable that pictures are cut off in hight?

are your images same size?

No - pictures are not same size.
If you look at the 4 pictures you can see that they are not the same height.
Could you maybe put all your questions in one reply, so that we do not need to wait for each other after every question?

I bit confused I see border around carousel what you want it to look like

thats not the border - thats just space/padding in the module position.
I have now set the border to 15 and made it purple. Now you can see that the picture is cut in size and the purple border is not showing.
The border I want is the same as i had with your free version - i only updated to get more options.

Add this to your main template css file:

div#header_hotslider div#slide-holder img {
max-width: 565px;
max-height: 230px;
margin: 15px;
}