I am lost on what you are referring to. What square logo? I don’t see any logo on your screenshot? Are you asking how to add a logo?
It would be beneficial if you put some more work in the topics you open by describing in more detail what you are after, so people can help you beter.
The total width of the sidebar is determined by this var --d-sidebar-width so you can try to narrow that down.
Im curious what your plan is for pages that aren’t the homepage then, say a topic page like this one? You want to keep the header on those pages and only “lower” them on the homepage? A mock to show your idea would help.