What I gathered is that if the gulf stream stops, warm water will no longer flow north and the ice sheets will grow explosively, triggering an ice age (the kind where thick ice sheets flow southwards). That would pretty much wipe out anything built in the northern half of Europe... although granted, I don't know if it was like a kilometer high ice sheet rolling our way or how fast it went in previous ice ages, it might be slow enough that it can be stopped and broken down before it causes damage.
This is 99% conjecture. The current climate models do not predict those kinds of changes and most don’t have the fidelity to do so. Even the best models can’t account for simple things like aerosol pollution and they don’t have the resolution to determine the behaviour of ocean or atmospheric currents.
Early onset of glaciation via warming instead of cooling. Counter intuitive idea.
It’s unclear that it would play out that way. One could look at what happened the last time it stopped to get some idea, but things are different this time. We have a lot more atmospheric CO2.