As far as you wondering about the rough finish of the grout: Typicality, you pack the joints overly full with grout, immediately “squeegee” the excess off with a clean grout float tilted up at 90 degrees to the tile face (but struck across the tiles at an angle to the grid of grout joints), allow the grout to slightly firm up, “shape” the grout with a slightly damp sponge wiped in continuous circles, then finally wiped clean with a clean sponge at an angle to the joints. But it appears that the joints weren’t packed with enough grout to begin with...or the grout float wasn’t clean enough when used to squeegee away the excess and caused too much grout to be pulled from the joint.
