Did you add the image as the “Featured Image” to the page that is set as your Front page?
Take a look at this and add it to your page similarly and save the page http://prntscr.com/fnwprc
In your footer where you see the “weird HOME” text – that should display your footer menu but I think you arranged the menu items in the wrong structure.
It’s easy to fix though so no worries:
Have a look at this screenshot: http://prntscr.com/fnwnwu
You need to add the menu items that you want displaying underneath each other as subitems (drag them a little bit to the right) and it should solve he display issue.