Customizing Storefront Homestore theme

Hello,

I just installed WordPress 4.4.2 (Czech) with latest Storefront and bought Homestore theme and WooCommerce Customizer. I want to build full width homepage with categories listing in this design: https://www.dropbox.com/s/ptq9z05t72c4oe4/swagat01.jpg?dl=0. However I have some difficulties with customizing the homepage:

1. The promo area under the main navigation I can do with text widget, however what if I want the user to manage the contet (text and background image) in the box, what would be best solution?

2. How can I activate categories listing in fullwidth layout? I can get categories in the Sidebar in Homepage layout, however if I choose Homepage design > Static page and choose Shop (fullwidth), there is no widget to display categories (with pictures) on the homepage. Right now I have just this: https://www.dropbox.com/s/b3endpka2vpaykt/Screenshot%202016-04-18%2010.41.58.png?dl=0 not sure what to change to get categories above the products…

3. How I’d be able to hide/remove the section titles such us Shop, Product teaser (text widget title) that automatically appears on homepage in the heading of each sections?

Thanks!