Sounds a lot like the houses I lived in as a kid, a succession of them which my parents did up and sold before moving onto the next. Depends how much you like the house I guess. As you say its old so it was never going to come with a clean bill of health. I'd be tempted to see what the structural engineer has to say. If they're happy enough the house is sound then you can think about what sort of discount to negotiate. Its definitely odd nobody has any record of the work but I can't see what would be gained by this unless it was a cash job between friends?
I feel like you definitely have the right to ask whether its been rented out and if you aren't satisfied with the answers that might be another red flag. They aren't unreasonable questions. Re the knotweed, not sure how big a deal it is but if its guaranteed for another 7 years and then you might have to get it dealt with again on an ongoing basis it might be fine. Is it the sort of house you were imagining living in forever? that said theres always others out there and everyone else is saying walk away, so maybe they're right; I think a lot of old houses do have some sort of issue that would be characterised as serious in a newer house though.
