Receipt doesn't necessarily prove its on this car he sold you, he could have sold or kept the k04 I would definitely be asking questions, for starters I don't know if your aware but that front mount intercooler isn't a quality forge front mount intercooler but in actual fact a cheap eBay intercooler with forge sprayed on the core...
The turbo intake pipe is standard and the loom you labelled as having snapped wires go to your n75 valve which controls the boost...