Oh yeah. Anything in DC will be packed for Memorial Day weekend even the local McDonald's. Advance Passes are required each weekend regardless of holiday. Advanced timed entry passes are released monthly on the first Wednesday at 9am. So check the website for those at that time. If you end up in a pinch same day timed passes are available at 6am that day which you can only get online through the website as well.
Most likely it will be very difficult. The website has a good guide to getting tickets in advance.
I'm not sure. I've never tried during a Holiday. One, I'm not sure if they are even open on Holidays and two, you would have to try and contact them to see. I can tell you that you do want to plan as early as possible because tickets run out quickly. Have fun. You will enjoy it.
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