Wordpress does in fact add a current class by default:
check where it says:
<li id="menu-item-1688" class="current-menu-item">
Within your source code.
Now as for the other item, this is a bit tricky.
There is two ways to do it assuming that you need the last item for styling.
Option #1 is with pure CSS using the last-of-type selector.
Option #2, is using the get_wp_nav_menu as opposed to wp_nav_menu
and once you are inside the foreach
, you compare it using count and the current index of said foreach
to add the css class dinamically.
Edit: If you are a bit new to Wordpress theming, I would definitely go with option number 1 despite not having full browser coverage.