ok so
1) after you assemble the pickaxe push e to pick it up. the one on the bench is not assembled yet even though it looks like it is.
2) i believe that's the smelter for the ores you get from the mine, though i have yet to try this out myself.
3) you have to have heated ingots on the anvil and be looking at it(or at least in it's general area, haven't tested yet) before you can make your selection, as the available selections change with the number of ingots.
hope this helps :)