Listing the scenarios as A-D, where A, B, and C are in the first spoiler and D is in the second one.
Scenario A:
As noted, gravity would still be pulling on the rod. It would accelerate downwards until it reached terminal velocity, which due to not having any air directly beneath it to exert any direct forces (leaving only shear ones) would be very fast.
Scenario B:
If we were basing it off the game's physics the portal pair would instantly be destabilized as soon as you started to move the orange portal (since that's what happens to portals on moving platforms in the game). This would then attempt to force the rod out of the portal, and being unable to do so, would slice it at the portal locations. If we assumed that you could move the portal without it destabilizing, then the rod would essentially "run into" itself and the force of the portal moving would cause it to buckle and bend as much as necessary to keep the whole rod's length between the portals (this would likely cost no additional force on the platform holding the portal, since it would be tapping into the energy of you breaking the fabric of space itself). If the portals actually met each other, you would run into scenario 4. IMO it's unlikely that the portal's movement would be stopped by the rod. In this case we are bending the fabric of space itself, which could certainly exert a tearing or compressing force on the rod. This force is, by contrast, much stronger than any sort of backwards force that the rod could conceivably exert, and as such would be the same as if we were compressing the rod with infinite force at a given speed.
Scenario C:
As mentioned in the first part of scenario B, judging by the game the portal would first attempt to shove the rod out on whichever side held the "majority" of the portal when the first set of portals closed (since opening a new portal is just a very fast combination of a "close old pair" + "open new pair" where one of the new pair is at the same location as before the close). Upon failing this, one would only surmise that it would cut the rod at a molecular level along the boundary of the portal, slicing between the individual molecules (possibly pushing some of them back out the blue portal temporarily). In this case since we moved the top portal, the unsupported rod would immediately fall downwards, launching it out of the new orange portal at an angle. (Should the rod be moving quickly while you did this, such as from scenario A, it would probably annihilate whatever was standing outside of the new orange portal location). If we instead removed the bottom portal the rod would simply fall over, or in the case of a fast moving rod, slam into the floor at whatever velocity it was falling.
Scenario D:
We would first encounter the same thing as in scenario B, where the man would essentially "run into" himself and be squished. Should the portals continue to be pushed together, he would eventually be ejected as a very fine paste out from between the two panels, possibly at a rather high speed.
Edit: Small clarification to my reasoning.
On the non-imaginary note though, real wormholes/portals would actually have a distance in between the two ends. That distance might be measured in micrometers, but such a distance would exist.