I imported the pre-built page Application and of course it imported it to /home-application. I want to set this as my home page and have a top horizontal menu... how do achieve that?
If you want to change home page to another, check this article https://codex.wordpress.org/Creating_a_Static_Front_Page
I have imported the page from the theme - Home - Application and set it as the home page according to the instructions in the link but no change.
I see Application demo page as home page on your site. To add menu you need create menu in "Appearance -> Menu" section.