Hello,
1. Browse categories element in the Header builder cannot be changed in width. At the same time, you can show this menu by means of Megamenu widget. So you create a row in the page content, set the column width as you need and show the menu in the page content as it has been implemented in this demo: https://woodmart.xtemos.com/demo-fashion/demo/fashion/dle4 Here is how it looks like in admin https://prnt.sc/tfx7fu You see, you can set any width for the column.
2. I have checked the site and I cannot figure out where do you want to move the bottom row, how do you want to locate it. If you want to put it into the top bar, just add these elements to the top bar. You will have to remove the elements which are there now to get the space enough. Please clarify.
3. You need to enable the base version and then change the logo and images. Make the full backup of your site! Please note: uploading a demo would rewrite all the theme settings and widgets. Please read and follow the instruction: https://xtemos.com/docs/woodmart/installation-process/
Best Regards