Clearances in most places are at or near 7". There are a few tighter areas, but those are usually limited to crossovers, not "parallel" operation. There are a few places that will have viaduct style elevated portions with a span or truss or something.
Here's an angle view where you can see the elevations. Note, Scarm does some weird things when tracks are near the edge of the board - the actual area is larger than this would show. Also, It doesn't let me line up tunnel entrances nor do ganged tunnels (which I plan on doing in the real thing).