Re: Pushing a portal through another portal.
OK, so say we do it in the way Xanthir mentioned. We put the orange portal on the wall, with the usual orientation, and the blue portal on an oval-shaped piece of wood, which we hold such that the major axis points toward the orange portal ("bottom" first), the minor axis is vertical, and the opening faces left.
Now, as we start shoving the blue portal through the orange portal, the bottom of the blue portal will stick out of the middle of the blue portal. It will be horizontal, opening down (if you stick the blue portal into the orange one "top" first, then it would be facing up. Interestingly, whether you hold the blue portal so it faces left or right would have no effect here). For convenience, I'll call the part of the blue portal that hasn't gone through the orange portal yet (the part we're holding) just "the blue portal", and the part of the blue portal that has gone through the orange portal "the second blue portal".
As we get the blue portal close to halfway through the orange portal, the second blue portal will have stuck out far enough to not fit through the orange portal, and will hit the wall. As you keep pushing forward, you'll feel something lifting the far end of the blue portal (the image of the wall as viewed through the orange portal is moving up, and the far end of the blue portal is resting on it). As the blue portal angles up, the second blue portal will angle towards you. Since the plane of the blue portal is still vertical, the second blue portal will also rotate to match the first blue portal, around the left-right axis (that is, your left and right, not any of the portals').
I'm not sure what will happen after this... the second blue portal is no longer perpendicular to the wall, so I think the forces will try to rotate it around its major axis... which'll do the same to the first blue portal, which'll twist it to be no longer vertical, and then the second blue portal will be sticking out at a strange angle... the 3D visualisation section of my brain is shutting down.
When I get home, I'll mock something up in Blender, so I can try to see what would happen...
While no one overhear you quickly tell me not cow cow.
but how about watch phone?