yes disney world is open on every holiday. they are open 365 days a year so every day.
the only reason they would close is if a event such as 9/11 happens or an extremely bad huricane. but that hasn't happened often. in fact disney world has only ever closed 4 times. three of which were due to really bad huricanes and one time was on 9/11 in fear that disney world may be attacked since soooo many people go there each day.
so when ever you go i wouldn't worry that it will close cuz its only closed 4 times since 1971.

and yes it is true that you can get in free on your b-day in 2009. and its not just for kids its for any one any age. and it must be on your b-day it can't be the day before or after or around the time of your b-day it has to be on the exact date.
here is the link to learn about it and register.
http://disneyparks.disney.go.com/disneyparks/en_US/WhatWillYouCelebrate/index?name=WDWCelebrationsOverviewPage