Goldfish have trailing feces, is it intestinal worms or something else?

[hatgirl_17]

I recently purchased 3 goldfish, two fantail and one black moor. Since the day I got them, I have been wondering if they were sick when I brought them home. I can't seem to get a straight answer about what goldfish feces are supposed to look like, so I'll describe (sorry) how my fish's feces look. They are long and thin, starting a brownish color and trailing off a clear-white color, getting thinner and more stringy at the end. They don't drop right away, they kind of trail behind the fish for a few minutes before floating to the bottom. Is this normal feces or are they worms, or constipation, or something? I feed them goldfish flakes, and only yesterday I have started soaking the flakes before feeding, just in case they are constipated. Help?
My black moor died! He was very listless/sluggish a couple of days after we brought them home. Then he started to swim up toward the corner of the tank, he would swim like that for hours throughout the day. Then he started losing momentum and would just sit at the bottom on the gravel. He came up for food, but that's about it. Then he stopped coming up for food this morning. We got home this evening and he was definitely dead, no question about it. I am worried that the feces might have been the issue, since there were no other physical signs of illness, and what if my other fish are also sick? I want to try to prevent them from dying! So if someone could help, that would be great!
Update: Good to know it wasn't the feces. I've tested the pH in the water, it was around 7.8, so I've begun to neutralize it. Temperature is around 71 degrees Fahrenheit. I have been doing partial water changes every other day, because I know I didn't put them in the tank in perfect conditions, but I can't go back and do it over, ya know? I bought fizz tablets to remove Ammonia and condition the water, which I will do at my next water change tomorrow (I've been removing chloramine and chlorine every water change thus far, we have city water). Once I get the water right, I will probably only do a water change once a week, but I realize the good bacteria is only starting to collect, so I need to be extra careful in the first month. It is only a 10 gallon tank, that is all we could afford and all that is practical for a small apartment. The two fish get along well and seem as happy as clams. Oh, we also have a Mystery Snail, which hasn't seemed to bother the goldfish one way or the other