>Tell me if there is any function in Javascript to check whether a date is valid or not.

Try the parse method of the Date object, if you pass it a string, it returns either the milliseconds since midnight 1/1/1970 if it is valid date or else NaN (check with isNaN()).

function CheckDate( DateString )
{
return( ! isNaN( Date.parse( DateString ) ) ) ;
}

>Also tell the events associated with < SELECT > for dropdown of the list box except for click ofcourse (something associated with the keyboard)

This site lists all evcents - click on the event you are interested in & you will get a list of tags that support that event.
http://www.blooberry.com/indexdot/html/tagpages/attributes/events.htm