Howdy y'all. So I am a new mustang owner. Finally got my favorite far but alas I'm stuck. I've read through Haynes book and tried to look up diagrams but with the set up that the previous owners had on the car, looks nothing like stock. It's a 1998 Mustang 3.8 Base

With the pictures, are these hoses necessary for completion? My car runs a bit rough. Cleaned out the Idle Control Valve so that helped it a bunch in running much smoother but these hoses make me wonder if I need to have them...

Heat Hose Break?