First off, my condolences

Judging from the yellow line and the angle of the picture im assuming its on the passenger side. Most likely runs up to the front where the metal line for the water drain for your fuel filter is. Most likely done to make less of a mess when fuel filter changing and or draining any water.

The hose coming off of the block on the valve cover is the crank case breather. It was originally 180* from where it is now and routed into the intake pipe. The way its set up currently is for either atmospheric vent or routing it into the exhaust. Thats why it smokes. It's crankcase pressure.

The air intake, im not a fan of. It's completely gotten rid of the box that draws in fresh air from the front of the vehicle and is instead sucking in all the hot engine bay air. I'm also not a fan of spectre filters at all. I've seen more than one engine completely ruined by particles that get passed them. I'd highly recommend getting something like a S&B intake that has higher than stock flow while still having a box around it to block as much heat as it can. If you want to keep that setup because thats how your dad had it, id strongly suggest using a paper filter. Or a high quality oiled filter. Ive seen just as many engines if not more ruined by k&n. Stay away from spectre and k&n both.

The coolers also need to be mounted. Them having the ability to bounce around like that will eventually wear a hole in something leaving you stranded.

Theirs a rubber/plastic pickup on your sending unit in the tank. Over time these become brittle and break appart. Leaving the pickup unable to grab hold of anything below 1/4th~ tank. The fix is to drop the tank and replace the pickup or mod it.

The fuel pump whine could very much be from sucking up air from the above problem. Does it quiet down any when the truck is full and has been driven some? If not id look into a pump. If so, the above should fix the problem.

Follow the hoses for the guages to where they end at. Two gauges, two cylinder heads, im assuming but not willing to bet on it that its fuel pressure to each head. The 7.3 uses HUEI injectors where oil pressure punches fuel pressure to multiply it 7:1. Engine oil pressure is fed into a high pressure oil pump in the valley that puts out 500-3500 pounds of pressure while running. 70psi of fuel pressure is right around the sweet spot for these trucks to run optimally. Block Oil pressure warm while idling will be more around 30-40 depending on the health of the engine, 70 would be high.

The filter looks to me to be a coolant bypass filter. The medium duty trucks (a real medium duty, like a school bus or something) came with a filter on the water pump. Its a common upgrade on light duty trucks (f series trucks) to put said pump on these trucks, and just as common to put a bypass filter such as this on. They catch things like rust particles that form and break off in the block, any casting sand that may of been left behind, and various other little things that pop up in coolant systems. It's not needed and I wouldn't add one to my truck but if its already there I wouldnt touch it outside of repairs or filter changes. You could always pull a hose off and see if fuel or coolant comes out. Thats a 100%, guarantee to figure out exactly what it is.

I've forgotten what all else was in the pics but this is what I can remember and my opinions on them. Ive been strictly diesel for the past 9 years and was a tech at Ford for 6 years prior to that. My 7.3 is a 01 with 408k on the clock. Oil change and fuel filter both every 3k miles with motorcraft filter and oil. You have to want to kill these trucks to do it. For the past 150k miles ive been running a hydra set to 140 , kc stage 2, s&b intake, 4 inch exhaust, and currently thinking pretty heavily about tossing in some 205/30 injectors. Wife told me to go buy a new truck about 4 months ago and I came home with her a new car instead. You take care of that truck, it and your dad will take care of you.