Yes, those aren't downtown apartments. There are many factors to consider, one of them being construction materials. Older buildings are made of bricks, at least here in Europe. The newer ones are prefabricated and built within months. If you compare 50 year old buildings to the new ones, for the same price you're getting underground garages, terraces, huge panoramic windows, and cheaper per square meter than a 50+ year old downtown apartments.
In my country, the older buildings are deliberately devalued, and most of the people buy it, but only to find out that the building will be soon collapsed by a bulldozer. IMO The Trump administration is doing its best to discourage people from moving to the US.
Yeah and other countries are promoting tourism,including mine and making the cost of living go only more higher. 
This is an important factor. The problem is that most EU countries have negative growth. Some have neutral, but a positive is a rarity.
I see why things are totally opposite in the EU. If I had the money I would try to own at least 4 apartments in big cities which would deliver a rent high enough to not have to work and live pretty comfortably. These will ALWAYS have a demand. In a globalized world there will always be people willing to pay for it. Many exchange students come to these cities if no locals want to rent it. There is a big demand. Just try to get them in places without troublesome people so you don't have to lose sleep over some fucktard destroying the furniture or whatnot.
Yeah don't do that. It seems to be a go to thing for a lot of people in my country and people do successfully do it, but its not ideal. Some people buy a 3 BHK and rent the two rooms and boom, they don't have to get a job. And the apartments will only be in demand, if they have their working environment around them, with essential stores around. You could earn a fuckton of money, but be careful, subletting is not allowed in some places.