1)2)3)4)-Please add following code into the custom.css:
.category-block{margin-right:0px!important;margin-left:30px}
.product_categories_grid :nth-child(1){margin-left:0px!important}
#menu-kategory li a{display:block;border-left:5px solid transparent;padding-left:5px;}
#menu-kategory li a:hover{border-left: 5px solid red;display:block!important;}
#menu-kategory li {padding:0;margin:0;}
#menu-kategory li:hover {padding:0;margin:0;background:grey;}
Regarding the slider please try to wrap all content(buttons and text) into the separate wrapping
With best regards
Brian Johnson