Hello,

1. To remove the icon please use this code:

.shopping-cart {
    position: relative;
    display: none!important;
}

2. In order to make the sub-menu background transparent use this code:

.basel-navigation .menu > li .sub-menu-dropdown {
    background-color: rgba(255,255,255,0.5);
}

Replace 0.5 for the value you need.

Best Regards