What is this dangling from the front driver's side and the cut hose?

If I remember right, that's normally mounted inside the fender and is merely a beeper. What cut hose? If you're talking about the corrugated plastic, that's just protective sleeving for the wires. The slit allows the wires to be placed inside.

 

Looks pretty gnarly now just unplug it and throw it out and leave the plug dangling I doubt it's working anyway It doesn't stop any show by not beeping or buzzing