Change size of textboxes in change address form

The size of the fields can be controlled with an option in the fields that you can edit via the menu Display->Custom fields.

It's big because there are long names in the dropdown.

You can fix the width of the dropdown by adding the CSS below in the front end CSS file of HikaShop via the Display tab of the configuration:
#address_country{
width : 150px;
}

If you want to change all of them, you can use such CSS:
.hikashop_checkout_login_right_part input, .hikashop_checkout_login_right_part select{
width : 150px !important;
}