I've done this. You do have to take the door frame out. It's easy. When you pull out the fridge, if you have the 110V/12V model like I do, it's just a couple of screws and it slides out. There are rails on the floor. I think I took the fridge door off as well to help when moving it. It's plugged into an outlet behind the fridge and wired directly for 12 V DC. Both easy to address. I found I needed to buy the same fridge as a replacement, because all of the fridges in that cubic foot range had different sizes and wouldn't fit properly without changing the size of the opening in some way. It was pretty easy to do if you are handy. Space availability makes it a bit clumsy. Since I replaced like for like it was harder to find and a bit more expensive.
As far as the stain, the holly & teak flooring was not well sealed by the factory and absorbs water, causing the staining. Perhaps the fridge defrosted at some point? Even if you wipe it up quickly or even spill water from the sink area you could get something similar. Is the refrigerator working fine? There is really nothing that would leak from it, unless your door seal wasn't tight, causing the fridge to defrost. I think it would be easier to check and replace the door seal. It could also be the water pipes for the sink leaking. I think that is more likely. Either way, I would pull the fridge and take a look. I don't believe it is the fridge causing this, unless there is a door seal issue like I mentioned earlier.
Mine is a norcold de-490. I have troubleshooting and parts manuals. There is no reference in the troubleshooting section to leaking water.