Changed coolant overflow bottle


I changed a crack coolant over bottle on 2006 Busa. But there is black hose above the cap I don't know where it connect too. Please help. The black hose at bottom of bottle is connected.
hose from the bottom of overflow goes to radiator

the other one runs down the front of the bottle towards the ground, it's for if the overflow bottle overflows
Does anyone know what's the best way to clean the brown sludge out of the bottom of the overflow tank??? Thanks, fxf
oil in air filter box

could anyone please tell my how oil gets into the air filter box, with a stock filter? ???