Hello,
1. You need to edit the parent container element for your widget and adjust row gap for inner elements. By doing this, you will proportionally reduce the spacing between all elements in the container.
2. There is no such option in our theme by default. You may need to use an extra plugin for this purpose, like ACF.
3. You need to find a specific header set for the checkout page and replace the logo there. You can find it in Dashboard -> WoodMart -> Header builder.
Translate the titles for this layout in Dashboard -> WoodMart -> Layouts.
As for the shipping address checkbox, it is a part of the WooCommerce plugin. You can change this option in the plugin’s settings.
4. Unfortunately, there is no such option in WooCommerce plugin.
5. You can use any plugin you want for this purpose.
Kind Regards