Setting or plugin for showing submenus horizontally under the main menu, and keep them after selection

Roee, there’s no particular setting or plugin to do that kind of stuff, it’s all about how your theme is designed and developed. You might be able to achieve this using some custom CSS if you’re good enough with that. Basically what you have to do is find out the :hover state of a particular menu and apply the same rules to when the entry has got the current_page_item class, which WordPress appends when using wp_nav_menu().