Hello,
Our theme is not slow. You have installed a lot of plugins, please check description of plugins and disable that you don’t really use, because every plugin slows down the site a bit.
Demo version that you installed uses Multiple headers, it means different headers for different pages. You changed the logo for the Default header, and it works on Shop and other pages – http://prntscr.com/101oj4j , but to be able to change the logo for Home page go to Multiple headers and edit this custom header – http://prntscr.com/101ok3l Watch this video about Multiple headers – https://youtu.be/BpeXfzNwkOc
As I can see, your Shop page works fine – http://prntscr.com/101onhm (when W3 Total Cache plugin is disabled) , settings of this page can be changed via Theme Options > WooCommerce > Shop. When W3 Total Cache is activated there are js errors in the browser console, it can be a conflict of an option with additional plugins. Please read this article – https://premium.wpmudev.org/blog/w3-total-cache-settings/ and play with settings of the Cache plugin. Contact the plugin support if you need any further assistance.
Regards