Hello,

1) Please try adding the Ajax Search element in the HTML Block you added as filter form.

Screenshot for Clarification: https://gyazo.com/da99e058360dbced223d0cea9023ae32

2) Please try adding the following Custom CSS in the Global Custom CSS area under Theme Settings >> Custom CSS.

nav.woocommerce-pagination.wd-pagination {
    padding-bottom: 50px;
}

Regards.
Xtemos Studios.