Stinky dark pee here could be a sign of dehydration. Did you figure out if Fluffy is the one that is having the stinky pee as well as the runny poo? Runny poo can lead to dehydration which can be a serious issue. It sounds like she's not doing very well if she's just sleeping all day.
I would limit her diet to only hay, water, and an infant rehydration drink. The pellets contain protein and carbs that can keep bad bacteria in the GI tract alive. Removing them and going to a very basic diet when a bunny has diarrhea is like giving a human the BRAT (bananas, rice, applesauce, toast) diet when they have diarrhea. **This is just a comparison--the BRAT diet is totally wrong for a bunny with diarrhea; it's only ok for people.**
The infant rehydration drink, if you can find it, will really help her get better. It should firm the poo up a little, reduce problems related to dehydration, and give her some more energy. Don't give human sports drinks--here in the US the product is called Pedialyte and in the UK it is called Dioralyte--not sure what it is in Canada. It should contain only a tiny bit of sugar, lots of electrolyes, and some artificial sweeteners. It should be in a pharmacy or grocery store in the baby health section. I would give her as much as she will take, in a second bowl in her cage, or via oral syringe. If she won't take it orally at all, I'd say at least 10mL every 2hrs, it's an emergency.
Keep an eye on her temperature too--if she is too hot or too cold she should NOT be syringe-fed, and should be taken to an emergency vet.
I don't want to scare you, but diarrhea can be really serious in young bunnies. Usually I say that if the bunny's less than a year, diarrhea is an immediate emergency because they can go downhill very fast. Whenever a bunny of any age is listless and not moving much, that is an immediate emergency. Dark urine as well, and the combination of all these things really would make it an emergency in my book. The reason is that the bacteria in the rabbit's GI tract are not well established in younger bunnies, and bad bacteria can overgrow the good ones more quickly in younger bunnies than older ones. The bad bacteria produce runny stools, leading to dehydration, and they also release bacterial toxins into the blood stream, which is another serious issue that can only be solved by a vet drug called Questran or a more difficult to find over the counter horse drug called Bio-Sponge. I had to buy this drug over the internet because it's so new that it's hard to find. Some horse vets do carry it, and in some rural areas of the US it can be bought at farm supply stores.
I would also look into a probiotic. In the US we use BeneBac (from a large pet store) or ProBios (from a farm supply store), but in Canada it seems to be hard to find these. Another option you can use is human acidophilus capsules. They're found at grocery and natural food stores. Don't give milk products containing acidophilus--just get the capsules and cut them open and give in water via oral syringe.
The fur thing is most likely fur mites because of location but I wouldn't worry so much about that right away--it is not an emergency.
