We don't ever know exactly how they did it unless they publish some blog posts or development papers about it but
chrun said:
How they store that amount of data
It is less data as you might think, I can imagine a few bytes per brick which are location, transform, color and ID, maybe 9 * 4 = 36 bytes per brick.
The map itself is a hightmap with some biome data like in Minecraft
chrun said:
How they draw lego elements
Like you draw every other mesh. In a far view LODs are used and if you come closer, they turn into more detailed meshes until you are really close. I can imagine that the pins on every brick are just bump-mapped like you do for wall details in modern 3D games.
A bump-map is just a texture that gives additional hints to the lighting system to proper illuminate small details without the need of an artist to model those details into the mesh.
chrun said:
Do they use simplified mesh for LODs
Every game uses LODs these days to be able to maximize performance and render depth.
chrun said:
What a type of algorithms used for that type of placing bricks?
As I said in the opening sentence, I don't know because they didn't published any details so far but you can read about how Minecraft and other Voxel-Type games solved their problems and we also have already long discussions here on GD.net about the topic