1. See the first listing under "Top Questions"--"Before You Post a Hotel Request....." If you return with specifics, we can make suggestions.
2. See the second listing under "Top Questions"--"How Do I Get From the Airport to D.C.?"
3. Unless you have a U.S. citizen relative or friend who can request tickets for you, you are pretty much out-of-luck. And, as Darrell mentioned, due to the holiday activities at the White House, it's unlikely there will be many, if any, tours during the time of your stay. So you may as well cross this activity off your list.
4. Answered by Warthog
5. As Darrell says, everything will be open during their regular hours over the time period that you are here. I suggest you do a search of the Washington D.C. forum for "Christmas in D.C." There are a ton of threads that will make suggestions of things to see and do. Some ideas off the top of my head are:
a. U.S. Capitol Tour--(Since the White House tour is likely out.) Anybody can request this. See: aoc.gov/guided-tours-buildings-capitol-hill
b. Visit the Botanical Gardens: This is mentioned on the above website, but you don't need a special tour for it. Even if you aren't a big "plant person" (like me), the display of poinsettias, the miniature train and the miniature versions of D.C. monuments created from natural materials sure put one in a holiday mood!
c. Zoolights--This is walk-through exhibit of lights at the National Zoo and it's free. Some of the animal houses are open and there are places to get hot chocolate, etc. to warm up. It's pretty and a lot of fun. …about.com/od/christmasevents/a/ZooLights.htm
d. Holiday Performances--Check the Kennedy Center website closer to your visit for a schedule of the Millennium Stage performances. They take place at 6pm every night and are free. Also, check Goldstar.com for discount tickets to performances. There's going to be some good stuff at the theatres this holiday season!
Edited: 9:41 am, October 22, 2012