So, in order:
1. The hamburger menu is active by default, it is just that it is activated through JavaScript, and as it is not a script that listen for the change of the size of the window (I don’t think it is necessary, usually users do not resize the window as a mobile in a desktop environment), it does not appear on the preview of the WordPress customizer. In any case, you can check it by using the inspector of your Web browser, by activating the mobile device simulator. Or simply by opening the website from a mobile device.
2. The theme links for the menu are customizable as in the demo, but it is not an option provided from the theme as of now. I tried to reproduce other aspects of W3CSS (you can find them by exploring the WordPress customizer).
In these days I am working on a block theme version of the theme, you can find a first basic support from yesterday evening. If I have time I would develop a block to show the menu as it appears in the demo you showed me.
Of course, you can change the theme also in its classic version by adding the W3CSS classes that you prefer.
Regards
