There weren't any border controls when I did it 3 years ago.
The current trrain works fine (although a tad expensive)
I don't see why a metro is needed
The border controls came on during the refugee crisis a little after that. While not a permanent feature, they serve to remind that neither Schengen nor the NPU is necessarily a permanent arrangement, and that Denmark and Sweden are different countries (and, perhaps more to the point, that, while Copenhagen is the capital of Denmark, Malmo is quite distant from Stockholm, so the implications of government policies aren't quite so immediately visible).
The train is fine for a casual traveller, but is wholly inadequate for commuters. The driver swap and extended wait at the Hovedbanegard is bad for commuters from Osterport and Norreport (a large chunk of the business areas). The route is rather indirect, taking a SW route through the city, the a sharp turn to the east to go through the airport. Even with a 10-minute headway (not sure if the bridge can cope with more) on double units, the trains are absolutely rammed at peak times, and local traffic flows interfere with the longer-distance ones (the airport traffic blocks the Malmo commuters, the Malmo commuters block those heading further afield in Skane). This also blocks the airport from serving more Danish inter-city services, and the bridge from serving more international inter-city services.
