Dear Nirag: For your first issue; you have no need to use the up or down arrows, as the only ones used for movement are left and right. For your second issue; Try clicking on the screen of the game, and see if that fixes the Spacebar issue. It has never once failed me. For your last complaint; I believe that was just noodlstudios way of putting a little creativity in his rather linear levels. Instead of thinking about it as a poor game design choice, think of it as a hidden secret! (This applies to the answer selection screen issue especially.)
Sincerely, Dairtheaccomplismnt.