First, if you go to Dashboard > Appearance > Menus and click Screen Options on the top right side, you'll see a drop down panel open. One option will be CSS Classes. Check it. Then click on Screen Options again.
When you add a custom menu item or open an existing one, you may now add a unique word or phrase with no spaces that can be custom styled with CSS.
Between the first three items and the next, you can add a new menu item and use a # for the link. Using the unique class, you may always set the width of that specific element.
As for making the logo... put that into the background, or, you can add it in several ways. I do not know quite how you'd make it layer over a slider. A link can be made with that logo, based on how it's added and by using z-index, I suspect, to make it work.