How to display date/ time of current user base on time zone?
You can modify the user pages (view/edit/etc) with the user templates, like the user profile template In the template's top documentation there's some good info like:

 * Use render($user_profile) to print all profile items, or print a subset
 * such as render($user_profile['user_picture']). Always call
 * render($user_profile) at the end in order to print all remaining items. 


So you can first dpm the $user_profile array and find out the user's timezone, then add php code after the print render($user_profile); to print the date/time according to the timezone value you retrieved from the user profile array.