3d tiles, cubes with different textures on each side

[ProNoob]

First of all I must say that my knowledge about 3d graphics is really really poor => total newbie.

I want to have such cube, so I can change texture of each side separately, becouse...

I need to create world made of 3d tiles. (like one in minecraft game)

Also there are gonna be multiple tiles with same but moving texture - for example water.
Texture's moving animation must be same on all cubes (ie for water to look like it flows in desired direction) so i thought objects should share texture matrix, but what if some tiles must have only one side rotated  or only texture on it rotated (but then it cannot share texture matrix)  not the whole cube

Also each side must be controlled separately, so if i put two half-transparent cubes next to each other(touching), i want them to "act as one" (the side that is "touching" i want not to display)

I would be thankful for any suggestions or hints.