Hi JB,
2. While it’s automatically calculated, you can decrease it by using a custom CSS with negative to margin, such as:
.asp_r {
margin-top: -12px !important;
}3. Unfortunately no, and there isn’t any custom code or bypass method to do that. The search bar would have to be in a fixed position in order to place an overlay below it. Moving static elements to fixed positions temporarily and vice versa via scripts is very problematic, at this point this is unfortunately not possible.