Any idea how to cut these two objects so that i get a connected tunnel to be able to walk through? I was able to cut the A part but not the B part of the tunnel.
You are on the right track with using the Boolean Modifier, you just have to use it on the "Lumpy Tunnel" as well.
Add a boolean to your tunnel, and select your staircase as the cut object. As you can see from the photos, the original placement of the staircase causes the bool to make some ugly cuts (Image 1), but if you move it .001 along the Y axis, it makes a cleaner bool operation (Image 2).
After applying the boolean, it's just a matter of cleanup. For me, the bool left a ring of duplicate faces on the inside of the "merged junction (Image 3). I deleted them, and then there was another ring of faces underneath. Select and delete them as well (Image 4).
The result should look like this: