For lighter customizations, go to Admin, Customize. There, you can inject CSS code, JavaScript and HTML into many parts of the site.
If you need more concrete help, it’s best if you start by creating mockups: Take screenshots of Discourse and use them to create a rough draft of what you want to achieve. This helps you organizing your thoughts and us knowing what you want 
Adding a persistent sidebar might be quite tricky – there may be no room there, especially on small or even mobile screens. I’d recommend that you either try showing these feeds on a separate page and only adding navigation elements to get there to the header (which is comparatively easy).
Alternatively, it might be more feasible to add these feeds only to a certain screen. For example, on larger screens, it might make sens to add this to Latest by shrinking the existing table horizontally and adding the feeds on the right:
This would require an alternative strategy for mobile, however.