Cement around decorative bricks leaves grey/matte coating on bricks
Q1: 

I would try a stiff brush and water.  If this does not work, you may be able to try a muriatic acid solution, but I would look at the manufacturer's recommendations first.  Depending on the brick color and type, this may discolor the brick.

Q2:


Apply the grout using a grout bag to minimize the mess.
When the joints are filled, wait until the grout is the consistency of wet beach sand.
Go over the joints with a brick jointer.  
As you are jointing, periodically wipe down the brick surface with a wet mason's sponge to remove any grout from the brick face (clean the sponge out in a bucket of water as you go).