Hi Amit,
The live search looks correct to me: http://i.imgur.com/B4elv4S.png
If I do a search the results are displayed in the column next to the settings. And the settings when activated display next to the results.
The results page (when redirected) cannot be styled via shortcodes, it is not possible. It does not matter if you place the results shortcode there, it’s not possible to use it to display the results on redirection with that shortcode. That page layout is fully controlled by the theme files.