Can't remove the Home link using CSS as of the current version of the theme. Consider using Custom Menu to define your own menu instead of using the default one. Also, in the next version, the default hardcoded Home link will no longer be displayed if a static front page is used.
...remove the page title from the top of each of my static pages?
Which page title do you want to remove? The want on the browser top bar or the page title on the page itself?