Hello,
1. Regarding the SVG Icons, can you please once check if you have installed the Safe SVG (https://wordpress.org/plugins/safe-svg/) plugin on your Site?
If yes and you are still facing the issue then can you please share the WP admin login details of your site so we will check and assist you accordingly.
2. To change the Background Color of the Browse Categories Menu, you need to go to Dashboard > Woodmart > Header Builder > there edit your Header > then edit the Categories Menu widget there > in that go to Colors tab > there you can define the Color under the Background Settings: https://ibb.co/z66xdV4
Best Regards.