The demo site of ours also has the same responsive behavior you mention. You couldn’t see the responsive version because of the iframe bar on the top. If you close that iframe, then you can see that the site behaves exactly as you mention about your site.
Besides, if you want to make your site look exactly as the pc version in the tablet, then you will have to make significant changes to the theme. Also you may run into lots of issues with certain sections not displaying properly in the tablet resolution.
Regarding, showing the desktop menu in the mobile resolution is not possible without disabling the responsive behavior completely, which will need significant code changes.