How big should a nav bar be?
Personally I feel most comfortable using a navbar height of 64px. It is enough height to accommodate a logo, and there is room enough to use text in combination with symbols.
How to set navbar full width?
The simplest way to get the effect you are looking for (for any number of buttons) is to use a table with a 100% width. A more complicated way is to give each button an equal percentage width such that with the number of buttons it adds up to 100%. You have 5 buttons, so you can put width:20%; on #nav ul li .
What is the purpose of a nav bar?
The purpose of a navigation bar is to help your user browse through your website effortlessly. A navigation bar is usually placed at the top of your website. On a mobile phone, the navigation bar is usually placed on your website's top left and looks like a hamburger or, as typically referred to – a hamburger button.