Geez, *****ing computers! I just wrote an answer for you and while checking at preview the whole f****ing thing vanished!
It looks like the old "replace parts until it is fixed" trick, or the owner says WTF is this!
This is the hose that goes from the turbo charger to the intercooler. It is under pressure from the turbo and at a higher temperature than ambient. (but not as hot as the exhaust gas)
This is a low pressure fuel hose, maybe from the filter to the high pressure injection pump. Unusual to fail unless mishandled.
This an electrical relay to energise the glow plugs, It may or may not have an inbuilt timer.
Was the engine hard to start? These are "glow plugs" used to pre-heat the air in the combustion chamber to aid starting. The system may or may not have a sensor that tells the ECU if they are required for each start.
I was not aware that these engines had them, as they are a cold climate requirement. Just my opinion, but I doubt if they are ever needed or used in this climate.
The rectangular gaskets may be from either the intercooler, or the inlet manifold. Not sure why there are 8 of them. Is there a part number? The big round gaskets are from where the big hose fits onto each end of the turbo and intercooler.
You mentioned previously that they showed you the turbo charger. There is nothing there that is part of the turbo, except maybe a gasket. If it was my car I think that I would be looking at replacing those hoses with silicone parts that I linked to previously.
Any questions please ask, as there is no such thing as a dumb question with things like this.