Are you saying you want to highlight the menu item corresponding to the section which is visible on the home page? I am afraid that is not possible without customizing the theme in a major way. Squash was not designed to be a full fledged single page theme.
No I don’t think so, when I click on a tab and don’t scroll so the sticky header is showing the writing on the current tab of the primary header changes colour (which is perfect). But if you do scroll down that page and the sticky header shows you don’t know what page you are on because the sticky header current tab isn’t highlighted.
As my site is currently under construction I have attached some screen shots.