QBSP.exe makes the Binary Space Partitioning for your map (hence B.S.P.) This is the core of your level geometry. I think it also adds other things like monsters and doors. QVIS.exe makes the information that lets the engine know what can and can't be seen. This prevents the computer from drawing everthing on screen, even what you can't see behind walls. QRAD.exe lights up the level with your light entities. Without using this, your map will be fully light with no dark corners.
As for using Quake 1 or 2 bsp's with the Irrlicht engine, I don't think Irrlicht has that support. Irrlicht DOES support Quake 3 bsp's though. You can find more information on their website at: http://irrlicht.sourceforge.net/features.html
The supported engine file types are near the bottom under Supported Formats with the picture of the pink cube. You should be able to use Tread to make Quake 3 Levels for the Irrlicht engine.