1) Some implementations render voxels as geometry, generated by various means. The mesh is constructed by approximating the surface of the volume described by the voxels. For this, you can look at the various implicit surface algorithms such as Marching Cubes, Marching Tetrahedrons, etc... Other implementations render the voxels using ray-casting, tracing screen-pixel rays and calculating intersections with the voxel data.

2) In voxel terrain, you need to store the various data points that comprise your voxel volume. Material, density/translucency, etc... The smaller and leaner you can make your voxel representation, the better.Many representations will go with a single byte material ID that allows, of course, 256 different types of materials.

3) Yep.

4) Yep. Although you can mitigate the memory usage by using data constructs such as Sparse Voxel Octree (SVO), data storage and access remains very much a limiting factor for large-scale usage of voxels.

5) This one can be a toughie. You can look into techniques such as tri-planar mapping to texture it.

6) Depends on how you decide to render it. Ken Silverman's Voxlap system doesn't use shaders, but the texturing isn't very high-def. For higher definition texturing, I suspect you probably will want to use shaders. A technique such as tri-planar mapping will require them.