The route line of the express trains does not lie in parallel to the slower train which stop at all stations. Can this be changed in any way?
When editing the route, you can set waypoints to tell the train where it should go without stopping.
I think the route lines on the network map just take a simple path with at most one bend. The route lines do not care whether they follow other routes that use the same tracks (or roads), which would explain the lack of parallel routing.
I'm not sure waypoints change the display of the network map
Network display on the minimap reflects waypoints.