Hi Igor,
The home page of the example site is using some kind of slider, it will require custom JavaScript which is out of the scope of this forum.
Or you can try using a slider plugin.
To merge the content with the menu, you can use a header element of GP, here’s a tutorial video:
https://youtu.be/TP8mgBQTgGg
To have hamburger menu icon on desktop, you can set the navigation mobile break point to a very high value, eg. 999999
at customizer > layout > primary navigation.