Yeah, that's a bridge over my channel. My miner decided to climb out of the filling channel on the wrong side, so I built a bridge to rescue her. I suppose I should be glad she didn't try swimming up the channel and drown.
The mountain river is a random distance from the mountain face. Sometimes I hit it a single screen's worth of digging, somtimes it's three or four. When you hit it there's a very good chance the water will rush out and flood your fortress, so I'd recommend just making a single dwarf dig east until you hit it. Crocodiles, frogmen, and the like can invade your fortress from the river, so you'll need to harden the areas that access the mountain river.
Immigrants are a nuisance! The number of immigrants is tied to how large and how swanky your fortress is. The dwarven traders that drop by carry back tales of your success. To prevent this, I hook my trade depot to my irrigation system and drown the traders after they finish unloading their wares. Dead dwarves tell no tales.
EDIT: God, they wish I would merely seize their goods.