Just on the issue of zooming in and out, that isn't part of the responsive design. Responsive is changing the layout to adapt to the viewing device. So on a full screen computer you don't have any layout changes but as you get to a smaller device it doesn't just shrink the whole page it instead responds to the new size constraints and changes the layout accordingly.
If you just want to zoom in and out on the page without it changing any layout, you can turn off that feature in Layout & Settings> Responsive Layout.
What this means for you and your site is that the current navigation menu you have is too long for the smaller tablet size and so the navigation items get wrapped to a second line. The layout doesn't yet say "this device is small enough to need just the mobile dropdown nav" so it shrinks the space and leaves the menu intact.
You could either turn off responsive layout or shorten the amount of links in your main menu to quickly fix the issue.