Suppose I am watching a video on YouTube and want to watch another video. Is there a way to go to the search bar directly with a keyboard shortcut? I don't want to grab my mouse, focus on the small bar and go back to the keyboard again.
If you are within the focus of Flash, all your keyboard shortcuts do not work. All of these are limited to Flash, so tab will switch between different features of the player. (See this Superuser question.)
If you do alt+tab and then alt+tab again to regain focus of the browser, your keyboard controls are back; maybe a single tab or couple of tabs after that will take you to YouTube search.