These code for Squarespace 7.1.

Add code to Design > Custom CSS

How to change Dropdown Menu Width

/* dropdown menu width */
.header-nav-folder-content {
    width: 500px !important;
}

To change specific dropdown, use this code

div.header-nav-item:nth-child(1) .header-nav-folder-content {
    width: 400px !important;
}

Note

1 here is the ordinal number of the Dropdown Title (Folder Title). Count from left to right.

Add an Arrow After Dropdown Title

/* Dropdown title arrow */
a.header-nav-folder-title:after {
    content: "\e009";
    font-family: 'squarespace-ui-font';
    position: relative;
    top: 2px;
}

Center Dropdown Menu under Title

/* Center dropdown */
.header-nav-folder-content {
    background-color: green !important;
    left: 50% !important;
    transform: TranslateX(-50%);
}

Dropdown Menu Transparent

div.header-nav-folder-content {
    background-color: transparent !important;
}

Dropdown Menu 2 Columns

div.header-nav-folder-content {
    column-count: 2;
}

to make 3, 4, 5 columns… just change number 2 to 3, 4 or 5

Horizontal Dropdown Menu

/* Nav dropdown */
.header-nav-folder-content {
    width: 100% !important;
    display: -webkit-box !important;
    display: -ms-flexbox !important;
    display: flex !important;
    -webkit-box-pack: center;
        -ms-flex-pack: center;
            justify-content: center;
    left: 50% !important;
    -webkit-transform: translateX(-50%);
        -ms-transform: translateX(-50%);
            transform: translateX(-50%);
}
.header-nav-folder-content div {
    margin-right: 20px;
}
.header-nav .header-nav-item--folder {
    position: static;
}

Change Folder/Dropdown Title Text to Burger Icon

a.header-nav-folder-title:after {
    font-size: 12px;
    content: "\e030";
    font-family: 'squarespace-ui-font';
    font-size: 50px;
}
a.header-nav-folder-title {
    font-size: 0;
}