Your questions are going to get answers that are going to create more questions, so this may be wordy but I'll try to post references and try to explain as much as I can.
1: it's hard to tell the type of nem that is, but it's most definitely bleached.
What is bleaching? Well it is related to the stuff you are seeing being excreted.
The brown stuff the nem is excreting is called zooxanthelle. Most animals in the ocean are photosynthetic because they are inhabited by a form of symbiotic protozoan. Some people will call it an algae, but that's not actually accurate. It is a photosynthetic dinoflagellate, not an algae. This Protozoa actually provides most photosynthetic marine inverts with 90-100% of their energy requirements and is responsible for the animals color. When the animal becomes stressed, it expels the Zooxanthelle. It also expels zooxanthelle normally as a way to regulate the amount it needs to utilize the light available. If the animal is being blasted with light, it needs less zoo to provide its needs, so it expels what it doesn't need. Under low light conditions, the animal will hold on to more zoo. As I said before, when an animal stresses out, it often expels too much zoo, and therefore it will be unable to get any energy at all from the light. It will also not have any coloration and will turn white which we call "bleaching".
So that nem looks like it doesn't have a speck of zoo left in it. Now the only way that the animal will have to meet its energy needs is food. You need to feed it multiple times. Probably daily if not more until the zoo population returns. Coloration is a good indication. It needs fed daily or more until the color returns.
What do I feed it you ask?
That nem is going to need a varied diet. Many people will feed chunks of food like shrimp, and that's fine, but a better recovery is going to come by doing the following:
Get a blender, a turkey baster and some freezer bags. Go to the grocery store, and your LFS and get all kinds of food goodies. Mysis, Scallops, krill, brine, shrimp, silversides, squid, fish of any kind (ocean fish obviously). Literally any and all sea dwelling creature that you can afford. Take it all home.
Throw all this stuff in the blender and chop it up. Don't purree it into liquid, but chop it up finely. Get your freezer bags and pour some into a freezer bag. Lay the bag down on the counter flat with a small section left open to help expel the air and try to make the thing lay flat with as little air as possible. Zip the bag closed when you are satisfied. It should look like a large, flat thin wafer now. Start putting them in the freezer flat. It should freeze into a thin brick of slop. Take them out and bust them up into small pieces. Now you should be able to take a small cube of slop, and thaw it in a small cup of tank water. You can then suck it up with the turkey baster, turn the pumps off and squirt it all over the nem. It will close up around it and eat it all. This is the perfect food for him.
2: why did your nem bleach in the first place?
It probably was under stress from the move. It's as simple as that. Often times just the transport of the animal is enough to make it expel all its zoo and you have to nurse them back to health as I described above. Since you say it was white when you bought it, it's likely it was bleached at that point.
3: your nitrates are too high. IME nems are pretty sensitive to nitrates and with it being that high, you are really facing an uphill climb nursing that nem back to health. Truthfully, with all you've listed I think you are way overstocked which is likely the reason for your nitrates being as high as they are. You need to try to get the nitrates under 5. Water changes, carbon dosing, bio pellets and manual removal of detritus will help. Not having a skimmer isn't helping you in this department either.
references:
Zooxanthelle:
https://books.google.com/books?id=hhcUJRSilwsC&pg=PA98#v=onepage&q&f=false
http://www.mhhe.com/biosci/genbio/tlw3/eBridge/Chp14/14_5.pdf
Nem care:
http://www.advancedaquarist.com/2006/11/tips
http://www.reefaquarium.com/2012/keeping-anemones/
Carbon dosing:
http://reefkeeping.com/issues/2008-08/nftt/
Nitrate control:
http://www.advancedaquarist.com/2003/8/chemistry
DIY fish food:
http://www.melevsreef.com/node/1616
Coral bleaching:
http://www.marinebiology.org/coralbleaching.htm
http://oceanservice.noaa.gov/facts/coral_bleach.html
