1: Yes you need to dig before you can build.
2: Yeah, the depth and gold numbers are for the whole 3x3 square.
3: Unique means you can only have one in the mine. You can build a tavern and gambling den in any order, and you get both rerolls. Each Carpenter and Blacksmith can be used on one die each turn.
4: You don't have to build from left to right, but you do have to dig to the row before you can build in it
I hope that helps!