There's a luggage storage place at the nearest train station, but I forget the name. Its about 10 mins walk to the east. 20usd per item per day.
Not likely as far as I know. How about checking your bags at the airport?
I dont believe there's anywhere at the museum entrance to leave your bag. They do perform a bag check at the entrance but I've onky ever seen purses/laptop bags never any rolling luggage. I left my bag with hotel reception (after checkout). Most hotels will hold your bag for you for a few hours
There is a security check...i think only thwy allow backpacks and small handbags
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