The blacksmith itself has no effects.
Just the same way a barrack is only for training troops, the blacksmith is only for upgrade them.
So, if you have two blacksmiths, you are able to upgrade two things at the same.
But thats all
And to answer your next question:
Upgrades doesnt depend on specific blacksmiths. Theyre depending on troops.
So, if you build a second blacksmith, you will find the same Upgrade-levels, like in your first one.